Topological structure of solution sets: current results
Archivum Mathematicum (2000)
- Volume: 036, Issue: 5, page 343-382
- ISSN: 0044-8753
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topGórniewicz, Lech. "Topological structure of solution sets: current results." Archivum Mathematicum 036.5 (2000): 343-382. <http://eudml.org/doc/248648>.
@article{Górniewicz2000,
author = {Górniewicz, Lech},
journal = {Archivum Mathematicum},
keywords = {fixed points; multivalued maps; inverse systems; acyclicity; topological structure; limit map; topological degree; admissible maps},
language = {eng},
number = {5},
pages = {343-382},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Topological structure of solution sets: current results},
url = {http://eudml.org/doc/248648},
volume = {036},
year = {2000},
}
TY - JOUR
AU - Górniewicz, Lech
TI - Topological structure of solution sets: current results
JO - Archivum Mathematicum
PY - 2000
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 036
IS - 5
SP - 343
EP - 382
LA - eng
KW - fixed points; multivalued maps; inverse systems; acyclicity; topological structure; limit map; topological degree; admissible maps
UR - http://eudml.org/doc/248648
ER -
References
top- 1. R. P. Agarwal, D. O’Regan, The solutions set of integral inclusions on the half line, Analysis (2000), 1–7. MR1759068
- 2. R. R. Akhmerov M. I. Kamenskii A. S. Potapov A. E. Rodkina, B. N. Sadovskii, Measures of Noncompactness and Condensing Operators,, (translated from Russian), Birkhauser, Berlin, 1992. (1992) MR1153247
- 3. J. Andres, On the multivalued Poincaré operators, TMNA 10 (1997), 171–182. (1997) Zbl0909.47038MR1646627
- 4. J. Andres G. Gabor, L. Górniewicz, Boundary value problems on infinite intervals, Trans. Amer. Math. Soc. 351 (1999), 4861–4903. (1999) MR1603870
- 5. J. Andres G. Gabor, L. Górniewicz, Topological structure of solution sets to multivalued asymptotic problems, Z. Anal. Anwendungen 18, 4 (1999), 1–20. (1999)
- 6. J. Andres G. Gabor, L. Górniewicz, Acyclicity of solutions sets to functional inclusions, Nonlinear Analysis TMA (to appear). MR1894303
- 7. J. Andres, L. Górniewicz, On the Banach contraction principle for multivalued mappings, Lecture Notes in Mathematics (to appear). MR1842872
- 8. J. Andres L. Górniewicz, M. Lewicka, Partially dissipative periodic processes, Banach Center Publ. 35 (1996), 109–118. (1996) MR1448430
- 9. G. Anichini, P. Zecca, Multivalued differential equations in a Banach space: an application to control theory, J. Optim. Th. Appl. 21 (1977), 477–486. (1977) MR0440144
- 10. N. Aronszajn, Le correspondant topologique de l’unicité dans la théorie des équations différentielles, Ann. Math. 43 (1942), 730–738. (1942) Zbl0061.17106MR0007195
- 11. Z. Artstein, Continuous dependence on parameters of solutions of operator equations, Trans. Amer. Math. Soc. 231 (1977), 143–166. (1977) MR0445351
- 12. A. Augustynowicz Z. Dzedzej, B. D. Gelman, The solution set to BVP for some functional differential inclusions, Set-Valued Analysis 6 (1998), 257–263. (1998) MR1669783
- 13. R. Bader, W. Kryszewski, On the solution sets of constrained differential inclusions with applications, Set Valued Anal. (to appear). Zbl0991.34011MR1863363
- 14. M. E. Ballotti, Aronszajn’s theorem for a parabolic partial differential equation, Non-linear Anal. TMA 9, No. 11 (1985), 1183–1187. (1985) Zbl0583.35053MR0813652
- 15. J. Bebernes, M. Martelli, On the structure of the solution set for periodic boundary value problems, Nonlinear Anal. TMA 4, No. 4 (1980), 821–830. (1980) Zbl0453.34019MR0582550
- 16. J. Bebernes, K. Schmitt, Invariant sets and the Hukuhara–Kneser property for systems of parabolic partial differential equations, Rocky Mount. J. Math. 7, No. 3 (1967), 557–567. (1967) MR0600519
- 17. R. Bielawski L. Górniewicz, S. Plaskacz, Topological approach to differential inclusions on closed sets of , , Dynamics Reported 1 (1992), 225–250. (1992)
- 18. D. Bielawski T. Pruszko, On the structure of the set of solutions of a functional equation with application to boundary value problems, Ann. Polon. Math. 53, No. 3 (1991), 201–209. (1991) MR1109588
- 19. A. W. Bogatyrev, Fixed points and properties of solutions of differential inclusions, Math. Sbornik 47 (1983), 895–909 (in Russian). (1983) MR0712098
- 20. A. Bressan A. Cellina, A. Fryszkowski, A class of absolute retracts in spaces of integrable functions, Proc. Amer. Math. Soc. 112 (1991), 413–418. (1991) MR1045587
- 21. F. E. Browder, C. P. Gupta, Topological degree and nonlinear mappings of analytic type in Banach spaces, J. Math. Anal. Appl. 26 (1969), 730–738. (1969) Zbl0176.45401MR0257826
- 22. J. Bryszewski L. Górniewicz, T. Pruszko, An application of the topological degree theory to the study of the Darboux problem for hyperbolic equations, J. Math. Anal. Appl. 76 (1980), 107–115. (1980) MR0586649
- 23. A. I. Bulgakov, L. N. Lyapin, Some properties of the set of solutions of a Volterra–Hammerstein integral inclusion, Diff. Uravni. 14, No. 8 (1978), 1043–1048. (1978) Zbl0433.45018MR0507406
- 24. A. I. Bulgakov, L. N. Lyapin, Certain properties of the set of solutions of the Volterra–Hammerstein integral inclusion, Differents. Uravn. 14, No. 8 (1978), 1465–1472. (1978) MR0507406
- 25. A. I. Bulgakov, L. N. Lyapin, On the connectedness of sets of solutions of functional inclusions, Mat. Sbornik 119, No. 2 (1982), 295–300. (1982) MR0675198
- 26. A. Cellina, On the existence of solutions of ordinary differential equations in a Banach space, Funkc. Ekvac. 14 (1971), 129–136. (1971) MR0304805
- 27. A. Cellina, On the local existence of solutions of ordinary differential equations, Bull. Acad. Polon. Sci. 20 (1972), 293–296. (1972) Zbl0255.34053MR0315237
- 28. A. Cellina, On the nonexistence of solutions of differential equations in nonreflexive spaces, Bull. Amer. Math. Soc. 78 (1972), 1069–1072. (1972) MR0312017
- 29. J. Chandra V. Lakshmikantham, A. R. Mitchell, Existence of solutions of boundary value problems for nonlinear second order systems in a Banach space, Nonlinear Anal. TMA 2 (1978), 157–168. (1978) MR0512279
- 30. S. N. Chow, J. D. Schur, An existence theorem for ordinary differential equations in Banach spaces, Bull. Amer. Math. Soc. 77 (1971), 1018–1020. (1971) MR0287127
- 31. S. N. Chow, J. D. Schur, Fundamental theory of contingent differential equations in Banach spaces, Trans. Amer. Math. Soc. 179 (1973), 133–144. (1973) MR0324162
- 32. M. Cichoń, I. Kubiaczyk, Some remarks on the structure of the solutions set for differential inclusions in Banach spaces, J. Math. Anal. Appl. 233 (1999), 597–606. (1999) MR1689606
- 33. A. Constantin, Stability of solution sets of differential equations with multivalued right hand side, J. Diff. Equs. 114 (1994), 243–252. (1994) Zbl0808.34013MR1302143
- 34. G. Conti W. Kryszewski, P. Zecca, On the solvability of systems of noncompact inclusions, Ann. Mat. Pura Appl. (4), 160 (1991), 371–408. (1991) MR1163216
- 35. G. Conti V. V. Obukhovskii, P. Zecca, On the topological structure of the solution set for a semilinear functional-differential inclusion in a Banach space, (Preprint). MR1448435
- 36. J.-F. Couchouron, M. Kamenskii, Perturbations d’inclusions paraboliques par des opérateurs condensants, C. R. Acad. Sci. Paris 320 (1995), Serie I. 1–6. (1995) MR1340059
- 37. H. Covitz S. B. Nadler, Jr., Multi-valued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5–11. (1970) MR0263062
- 38. K. Czarnowski, Structure of the set of solutions of an initial-boundary value problem for a parabolic partial differential equations in an unbounded domain, Nonlinear Anal. TMA 27, no. 6 (1996), 723–729. (1996) MR1399071
- 39. K. Czarnowski, On the structure of fixed point sets of ’k-set contractions’ in spaces, Demonstratio Math. 30 (1997), 233–244. (1997) MR1469589
- 40. K. Czarnowski, T. Pruszko, On the structure of fixed point sets of compact maps in spaces with applications to integral and differential equations in unbounded domain, J. Math. Anal. Appl. 154 (1991), 151–163. (1991) MR1087965
- 41. J. L. Davy, Properties of the solution set of a generalized differential equations, Bull. Austr. Math. Soc. 6 (1972), 379–389. (1972) MR0303023
- 42. F. S. De Blasi, Existence and stability of solutions for autonomous multivalued differential equations in a Banach space, Rend. Accad. Naz. Lincei, Serie VII, 60 (1976), 767–774. (1976) MR0481328
- 43. F. S. De Blasi, On a property of the unit sphere in a Banach space, Bull. Soc. Math. R. S. Roumaine 21 (1977), 259–262. (1977) Zbl0365.46015MR0482402
- 44. F. S. De Blasi, Characterizations of certain classes of semicontinuous multifunctions by continuous approximations, J. Math. Anal. Appl. 106, No. 1 (1985), 1–8. (1985) Zbl0574.54012MR0780314
- 45. F. S. De Blasi L. Górniewicz, G. Pianigiani, Topological degree and periodic solutions of differential inclusions, Nonlinear Anal. TMA 37 (1999), 217–245. (1999) MR1689752
- 46. F. S. De Blasi, J. Myjak, On the solutions sets for differential inclusions, Bull. Polon. Acad. Sci. 33 (1985), 17–23. (1985) Zbl0571.34008MR0798723
- 47. F. S. De Blasi, J. Myjak, O, n the structure of the set of solutions of the Darboux problem for hyperbolic equations, Proc. Edinburgh Math. Soc., Ser. 2 29, No. 1 (1986), 7–14. (1986) MR0829175
- 48. F. S. De Blasi, G. Pianigiani, On the solution sets of nonconvex differential inclusions, J. Diff. Equs. 128 (1996), 541–555. (1996) Zbl0853.34013MR1398331
- 49. F. S. De Blasi, G. Pianigiani, Solution sets of boundary value problems for nonconvex differential inclusions, Nonlinear Anal. TMA 1 (1993), 303–313. (1993) Zbl0785.34018MR1233098
- 50. F. S. De Blasi G. Pianigiani, V. Staicu, Topological properties of nonconvex differential inclusions of evolution type, Nonlinear Anal. TMA 24 (1995), 711–720. (1995) MR1319080
- 51. K. Deimling, Periodic solutions of differential equations in Banach spaces, Man. Math. 24 (1978), 31–44. (1978) Zbl0373.34032MR0499551
- 52. K. Deimling, Open problems for ordinary differential equations in a Banach space, (in the book: Equationi Differenziali), Florence, 1978. (1978)
- 53. K. Deimling, M. R. Mohana Rao, On solutions sets of multivalued differential equations, Applicable Analysis 30 (1988), 129–135. (1988)
- 54. R. Dragoni J. W. Macki P. Nistri, P. Zecca, Solution Sets of Differential Equations in Abstract Spaces, Pitman Research Notes in Mathematics Series, 342, Longman, Harlow, 1996. (1996) MR1427944
- 55. J. Dubois, P. Morales, On the Hukuhara–Kneser property for some Cauchy problems in locally convex topological vector spaces, Lecture Notes in Math. vol. 964, pp. 162–170, Springer, Berlin, 1982. (1982) Zbl0509.34062MR0693110
- 56. J. Dubois, P. Morales, Structure de l’ensemble des solutions du probléme dee Cauchy sous le conditions de Carathéodory, Ann. Sci. Math. Quebec 7 (1983), 5–27. (1983) MR0699983
- 57. G. Dylawerski, L. Górniewicz, A remark on the Krasnosielskii translation operator, Serdica Math. J. 9 (1983), 102–107. (1983) MR0725816
- 58. Z. Dzedzej, B. Gelman, Dimension of the solution set for differential inclusions, Demonstration Math. 26 (1993), 149–158. (1993) Zbl0783.34008MR1226553
- 59. V. V. Filippov, The topological structure of spaces of solutions of ordinary differential equations, Uspekhi Mat. Nauk 48 (1993), 103–154. (in Russian) (1993) MR1227948
- 60. G. Gabor, On the acyclicity of fixed point sets of multivalued maps, TMNA 14 (1999), 327–343. (1999) MR1766183
- 61. B. D. Gelman, On the structure of the set of solutions for inclusions with multivalued operators, in Global Analysis - Studies and Applications III, (ed. Yu. G. Borisovich and Yu. E. Glikhlikh), Lecture Notes in Math. vol. 1334, pp. 60–78, Springer, Berlin, 1988. (1988) MR0964695
- 62. B. D. Gelman, Topological properties of fixed point sets of multivalued maps, Mat. Sb. 188, No. 12 (1997), 33–56. (1997) MR1607367
- 63. A. N. Godunov, A counter example to Peano’s Theorem in an infinite dimensional Hilbert space, Vestnik Mosk. Gos. Univ., Ser. Mat. Mek. 5 (1972), 31–34. (1972)
- 64. A. N. Godunov, Peano’s Theorem in an infinite dimensional Hilbert space is false even in a weakened form, Math. Notes 15 (1974), 273–279. (1974) MR0352640
- 65. K. Goebel, W. Rzymowski, An existence theorem for the equation x = f (t, x) in Banach spaces, Bull. Acad. Polon. Math. 18 (1970), 367–370. (1970) MR0269957
- 66. L. Górniewicz, Topological approach to differential inclusions, in: A. Granas and H. Frigon eds., NATO ASI Series C 472, Kluwer, 1975. (1975)
- 67. L. Górniewicz, Homological methods in fixed point theory of multivalued mappings, Dissertationes Math. 129 (1976), 1–71. (1976)
- 68. L. Górniewicz, On the solution sets of differential inclusions, J. Math. Anal. Appl. 113 (1986), 235–244. (1986) MR0826673
- 69. L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Kluwer, Dordrecht, 1999. (1999) MR1748378
- 70. L. Górniewicz, S. A. Marano, On the fixed point set of multivalued contractions, Rend. Circ. Mat. Palermo 40 (1996), 139–145. (1996) MR1407087
- 71. L. Górniewicz S. A. Marano, M. Slosarski, Fixed points of contractive multivalued maps, Proc. Amer. Math. Soc. 124 (1996), 2675–2683. (1996) MR1317038
- 72. L. Górniewicz P. Nistri, V. V. Obukovskii, Differential inclusions on proximate retracts of Hilbert spaces, Int. J. Nonlinear Diff. Equs. TMA 3 (1980), 13–26. (1980)
- 73. L. Górniewicz, T. Pruszko, On the set of solutions of the Darboux problem for some hyperbolic equations, Bull. Acad. Polon. Math. 28, No. 5-6 (1980), 279–286. (1980) MR0620202
- 74. L. Górniewicz, M. Slosarski, Topological and differential inclusions, Bull. Austr. Math. Soc. 45 (1992), 177–193. (1992) MR1155476
- 75. G. Haddad, Topological properties of the sets of solutions for functional differential inclusions, Nonlinear Anal. TMA 5, No. 12 (1981), 1349-1366. (1981) Zbl0496.34041MR0646220
- 76. A. J. Heunis, Continuous dependence of the solutions of an ordinary differential equation, J. Diff. Eqns. 54 (1984), 121–138. (1984) Zbl0547.34007MR0757289
- 77. C. J. Himmelberg, F. S. Van Vleck, On the topological triviality of solution sets, Rocky Mountain J. Math. 10 (1980), 247–252. (1980) Zbl0456.34004MR0573874
- 78. C. J. Himmelberg, F. S. Van Vleck, A note on the solution sets of differential inclusions, Rocky Mountain J. Math. 12 (1982), 621–625. (1982) Zbl0531.34007MR0683856
- 79. T. S. Hu, N. S. Papageorgiou, On the topological regularity of the solution set of differential inclusions with constrains, J. Diff. Equat. 107 (1994), 280–289. (1994) MR1264523
- 80. M. Hukuhara, Sur les systémes des équations differentielles ordinaires, Japan J. Math. 5 (1928), 345–350. (1928)
- 81. D. M. Hyman, On decreasing sequence of compact absolute retracts, Fund. Math. 64 (1959), 91–97. (1959) MR0253303
- 82. J. Jarník, J. Kurzweil, On conditions on right hand sides of differential relations, Časopis pro Pěst. Mat. 102 (1977), 334–349. (1977) MR0466702
- 83. M. I. Kamenskii, On the Peano Theorem in infinite dimensional spaces, Mat. Zametki 11, No. 5 (1972), 569–576. (1972) MR0304808
- 84. M. I. Kamenskii, V. V. Obukovskii, Condensing multioperators and periodic solutions of parabolic functional - differential inclusions in Banach spaces, Nonlinear Anal. TMA 20 (1991), 781–792. (1991) MR1214743
- 85. R. Kannan J. J. Nieto, M. B. Ray, A class of nonlinear boundary value problems without Landesman–Lazer condition, J. Math. Anal. Appl. 105 (1985), 1–11. (1985) MR0773569
- 86. A. Kari, On Peano’s Theorem in locally convex spaces, Studia Math. 73, No. 3 (1982), 213–223. (1982) Zbl0507.34047MR0675425
- 87. W. G. Kelley, A Kneser theorem for Volterra integral equations, Proc. Amer. Math. Soc. 40, No. 1 (1973), 183–190. (1973) Zbl0244.45003MR0316983
- 88. M. Kisielewicz, Multivalued differential equations in separable Banach spaces, J. Optim. Th. Appl. 37, No. 2 (1982), 231–249. (1982) Zbl0458.34008MR0663523
- 89. H. Kneser, Über die Lösungen eine system gewöhnlicher differential Gleichungen das der lipschitzchen Bedingung nicht genügt, S. B. Preuss. Akad. Wiss. Phys. Math. Kl. 4 (1923), 171–174. (1923)
- 90. A. Kolmogorov, S. Fomin, Elements of the Theory of Functions and Functional Analysis, Graylock, New York, 1957. (1957) MR0085462
- 91. M. A. Krasnoselskii P. P. Zabreiko, Geometrical Methods of Nonlinear Analysis, Springer-Verlag, Heidelberg 1984. (1984) MR0736839
- 92. W. Kryszewski, Topological and approximation methods in the degree theory of set-valued maps, Dissertationes Math. 336 (1994), 1–102. (1994) MR1307460
- 93. P. Krbec, J. Kurzweil, Kneser’s theorem for multivalued, differential delay equations, Časopis pro Pěst. Mat. 104, No. 1 (1979), 1–8. (1979) Zbl0405.34059MR0523570
- 94. Z. Kubíček, A generalization of N. Aronszajn’s theorem on connectedness of the fixed point set of a compact mapping, Czech. Math. J. 37, No. 112 (1987), 415–423. (1987) MR0904769
- 95. Z. Kubíček, On the structure of the fixed point sets of some compact maps in the Fréchet space, Math. Bohemica 118 (1993), 343–358. (1993)
- 96. Z. Kubíček, On the structure of the solution set of a functional differential system on an unbounded interval, Arch. Math. (Brno) 35 (1999), 215–228. (1999) MR1725839
- 97. I. Kubiaczyk, Structure of the sets of weak solutions of an ordinary differential equation in a Banach space, Ann. Polon. Math. 44, No. 1 (1980), 67–72. (1980) MR0764805
- 98. I. Kubiaczyk, Kneser’s Theorem for differential equations in Banach spaces, J. Diff. Equs. 45, No. 2 (1982), 139–147. (1982) MR0665991
- 99. I. Kubiaczyk, S. Szufla, Kneser’s Theorem for weak solutions of ordinary differential equations in Banach spaces, Publ. Inst. Math. (Beograd) (NS) 32, No. 46 (1982), 99–103. (1982) MR0710975
- 100. A. Lasota, J. A. Yorke, The generic property of existence of solutions of differential equations in Banach spaces, J. Diff. Equs. 13 (1973), 1–12. (1973) MR0335994
- 101. J. M. Lasry, R. Robert, Analyse Non Linéaire Multivoque, Cahiers de Math. de la Decision, Paris, No. 7611, 1977. (1977)
- 102. J. M. Lasry, R. Robert, Acyclicité de l’ensemble des solutions de certaines équations fonctionnelles, C. R. Acad. Sci. Paris 282, No. 22A (1976), 1283–1286 MR0436195
- 103. T. C. Lim, On fixed point stability for set valued contractive mappings with applications to generalized differential equations, J. Math. Anal. Appl. 110 (1985), 436–441. (1985) MR0805266
- 104. T. Ma, Topological degrees of set-valued compact fields in locally convex spaces, Dissertationes Math. XCII (1972), 1–47. (1972) MR0309103
- 105. S. Marano, V. Staicu, On the set of solutions to a class of nonconvex nonclosed differential inclusions, Acta Math. Hungarica 76 (1997), 287–301. (1997) Zbl0907.34010MR1459237
- 106. A. Margheri, P. Zecca, A note on the topological structure of solution sets of Sturm–Liouville problems in Banach spaces, Atti Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Math. Nat., (to appear).
- 107. H. Monch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal. TMA 4 (1980), 985–999. (1980) MR0586861
- 108. H. Monch, G. von Harten, On the Cauchy problem for ordinary differential equations in Banach spaces, Arch. Math. 39 (1982), 153–160. (1982) MR0675655
- 109. A. M. Muhsinov, On differential inclusions in a Banach space, Soviet Math. Dokl. 15 (1974), 1122–1125. (1974)
- 110. J. J. Nieto, Periodic solutions of nonlinear parabolic equations, J. Diff. Equs. 60, No. 1 (1985), 90–102. (1985) Zbl0537.35049MR0808259
- 111. J. J. Nieto, Nonuniqueness of solutions of semilinear elliptic equations at resonance, Boll. Un. Mat. Ital. 6, 5-A, No. 2, (1986), 205–210. (1986) MR0850289
- 112. J. J. Nieto, Structure of the solution set for semilinear elliptic equations, Colloq. Math. Soc. Janos Bolyai, 47 (1987), 799–807. (1987) Zbl0654.35035MR0890578
- 113. J. J. Nieto, Hukuhara–Kneser property for a nonlinear Dirichlet problem, J. Math. Anal. Appl. 128 (1987), 57–63. (1987) Zbl0648.34019MR0915966
- 114. J. J. Nieto, Decreasing sequences of compact absolute retracts and nonlinear problems, Boll. Un. Mat. Ital. 2-B, No. 7 (1988), 497–507. (1988) Zbl0667.47035MR0963315
- 115. J. J. Nieto, Aronszajn’s theorem for some nonlinear Dirichlet problem, Proc. Edinburg Math. Soc. 31 (1988), 345–351. (1988) MR0969064
- 116. J. J. Nieto, Nonlinear second order periodic value problems with Carathéodory functions, Appl. Anal. 34 (1989), 111–128. (1989)
- 117. J. J. Nieto, Periodic Neumann boundary value problem for nonlinear parabolic equations and application to an elliptic equation, Ann. Polon. Math. 54, No. 2 (1991), 111–116. (1991) Zbl0737.35032MR1104733
- 118. J. J. Nieto, L. Sanchez, Periodic boundary value problems for some Duffing equations, Diff. and Int. Equs. 1, No. 4 (1988), 399–408. (1988) MR0945817
- 119. V. V. Obukhovskii, Semilinear functional differential inclusions in a Banach space and controlled parabolic systems, Soviet J. Automat. Inform. Sci. 24, No. 3 (1991), 71–79. (1991) MR1173399
- 120. C. Olech, On the existence and uniqueness of solutions of an ordinary differential equation in the case of a Banach space, Bull. Acad. Polon. Math. 8 (1969), 667–673. (1969) MR0147733
- 121. N. S. Papageorgiou, Kneser’s Theorem for differential equations in Banach spaces, Bull. Austral. Math. Soc. 33, No. 3 (1986), 419–434. (1986) MR0837488
- 122. N. S. Papageorgiou, On the solution set of differential inclusions in a Banach space, Appl. Anal. 25, No. 4 (1987), 319–329. (1987) MR0912190
- 123. N. S. Papageorgiou, A property of the solution set of differential inclusions in Banach spaces with a Carathéodory orientor field, Appl. Anal. 27, No. 4 (1988), 279–287. (1988) MR0936472
- 124. N. S. Papageorgiou, On the solution set of differential inclusions with state constraints, Appl. Anal. 31 (1989), 279–289. (1989) Zbl0698.34015MR1017517
- 125. N. S. Papageorgiou, Convexity of the orientor field and the solution set of a class of evolution inclusions, Math. Slovaca 43 (1993), no. 5, 593–615. (1993) MR1273713
- 126. N. S. Papageorgiou, On the properties of the solution set of nonconvex evolution inclusions of the subdifferential type, Comment. Math. Univ. Carolin. 34 (1993), no. 4, 673–687. (1993) Zbl0792.34014MR1263796
- 127. N. S. Papageorgiou, A property of the solution set of nonlinear evolution inclusions with state constraints, Math. Japon. 38 (1993), no. 3, 559–569. (1993) Zbl0777.34043MR1221027
- 128. N. S. Papageorgiou, On the solution set of nonlinear evolution inclusions depending on a parameter, Publ. Math. Debrecen 44 (1994), no. 1–2, 31–49. (1994) Zbl0824.34018MR1269967
- 129. N. S. Papageorgiou, On the solution set of nonconvex subdifferential evolution inclusions, Czechoslovak Math. J. 44 (1994), no. 3, 481–500. (1994) Zbl0868.34010MR1288166
- 130. N. S. Papageorgiou, On the topological regularity of the solution set of differential inclusions with constraints, J. Diff. Equs. 107 (1994), no. 2, 280–289. (1994) Zbl0796.34017MR1264523
- 131. N. S. Papageorgiou, On the topological properties of the solution set of evolution inclusions involving time-dependent subdifferential operators, Boll. Un. Mat. Ital. 9 (1995), no. 2, 359–374. (1995) Zbl0845.34066MR1333967
- 132. N. S. Papageorgiou, On the properties of the solution set of semilinear evolution inclusions, Nonlinear Anal. TMA 24 (1995), no. 12, 1683–1712. (1995) Zbl0831.34014MR1330643
- 133. N. S. Papageorgiou, Topological properties of the solution set of integrodifferential inclusions, Comment. Math. Univ. Carolin. 36 (1995), no. 3, 429–442. (1995) Zbl0836.34019MR1364483
- 134. N. S. Papageorgiou, On the solution set of nonlinear integrodifferential inclusions in , , Math. Japon. 46 (1997), no. 1, 117–127. (1997) MR1466124
- 135. N. S. Papageorgiou, Topological properties of the solution set of a class of nonlinear evolutions inclusions, Czechoslovak Math. J. 47 (1997), no. 3, 409–424. (1997) MR1461421
- 136. N. S. Papageorgiou, On the structure of the solution set of evolution inclusions with time-dependent subdifferentials, Rend. Sem. Mat. Univ. Padova 97 (1997), 163–186. (1997) Zbl0893.34060MR1476169
- 137. N. S. Papageorgiou, F. Papalini, On the structure of the solution set of evolution inclusions with time-dependent subdifferentials, Acta Math. Univ. Comenian. (N.S.) 65 (1996), no. 1, 33–51. (1996) Zbl0865.34049MR1422293
- 138. N. S. Papageorgiou N. Shahzad, Properties of the solution set of nonlinear evolution inclusions, Appl. Math. Optim. 36 (1997), no. 1, 1–20. (1997) MR1446789
- 139. G. Peano, Sull’integrabilité delle equazioni differenziali del primo ordine, Atti della Reale Accad. dell Scienze di Torino 21 (1886), 677–685.
- 140. G. Peano, Démonstration de l’integrabilite des équations differentielles ordinaires, Mat. Annalen 37 (1890), 182–238.
- 141. W. V. Petryshyn, Note on the structure of fixed point sets of 1-set–contractions, Proc. Amer. Math. Soc. 31 (1972), 189–194. (1972) MR0285944
- 142. G. Pianigiani, Existence of solutions of ordinary differential equations in Banach spaces, Bull. Acad. Polon. Math. 23 (1975), 853–857. (1975) MR0393710
- 143. S. Plaskacz, On the solution sets for differential inclusions, Boll. Un. Mat. Ital. 7, 6-A (1992), 387–394. (1992) Zbl0774.34012MR1196133
- 144. J. Saint Raymond, Multivalued contractions, Set-Valued Analysis 2, 4 (1994), 559–571. (1994) Zbl0820.47065MR1308485
- 145. B. Ricceri, Une propriété topologique de l’ensemble des points fixes d’une contraction multivoque à valeurs convexes, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 81 (1987), 283–286. (1987) MR0999821
- 146. B. N. Sadovskii, On measures of noncompactness and contracting operators, in Problems in the Mathematical Analysis of Complex Systems, second edition, Voronezh (1968), 89–119. (in Russian) (1968) MR0301582
- 147. B. N. Sadovskii, Limit-compact and condensing operators, Uspekh. Mat. Nauk 27 (1972), 1–146. (in Russian) (1972) MR0428132
- 148. K. Schmitt, P. Volkmann, Boundary value problems for second order differential equations in convex subsets in a Banach space, Trans. Amer. Math. Soc. 218 (1976), 397–405. (1976) MR0397110
- 149. V. Šeda, Fredholm mappings and the generalized boundary value problem, Diff. Integral Equs. 8 (1995), 19–40. (1995) MR1296108
- 150. V. Šeda, Generalized boundary value problems and Fredholm mappings, Nonlinear Anal. TMA 30 (1997), 1607-1616. (1997) MR1490083
- 151. V. Šeda, Rδ -set of solutions to a boundary value problem, TMNA, (to appear).
- 152. J. S. Shin, Kneser type theorems for functional differential equations in a Banach space, Funk. Ekvacioj 35 (1992), 451–466. (1992) Zbl0785.34049MR1199467
- 153. Z. Song, Existence of generalized solutions for ordinary differential equations in Banach spaces, 3. Math. Anal. Appl. 128 (1987), 405–412. (1987) Zbl0666.34068MR0917374
- 154. W. Sosulski, Compactness and upper semi continuity of solution set of functional differential equations of hyperbolic type, Comment. Mat. Prace. Mat. 25, No. 2 (1985), 359–362. (1985) MR0844652
- 155. V. Staicu, Qualitative propeties of solutions sets to Lipschitzian differential inclusions, World Sci. Publ. (Singapore 1993), 910–914. (1993) MR1242362
- 156. S. Szufla, Some remarks on ordinary differential equations in Banach spaces, Bull. Acad. Polon. Math. 16 (1968), 795–800. (1968) MR0239238
- 157. S. Szufla, Measure of noncompactness and ordinary differential equations in Banach spaces, Bull Acad. Polon. Sci. 19 (1971), 831–835. (1971) MR0303043
- 158. S. Szufla, Structure of the solutions set of ordinary differential equations in a Banach space, Bull. Acad. Polon. Sci. 21, No. 2 (1973), 141–144. (1973) MR0333390
- 159. S. Szufla, Solutions sets of nonlinear equations, Bull. Acad. Polon. Sci. 21, No. 21 (1973), 971–976. (1973) MR0344959
- 160. S. Szufla, Some properties of the solutions set of ordinary differential equations, Bull. Acad. Polon. Sci. 22, No. 7 (1974), 675–678. (1974) MR0355245
- 161. S. Szufla, On the structure of solutions sets of differential and integral equations in Banach spaces, Ann. Polon. Math. 34 (1977), 165–177. (1977) MR0463608
- 162. S. Szufla, On the equation x = f (t, x) in Banach spaces, Bull. Acad. Polon. Sci. 26, No. 5 (1978), 401–406. (1978) MR0499578
- 163. S. Szufla, Kneser’s theorem for weak solutions of ordinary differential equations in reflexive Banach spaces, Bull. Acad. Polon. Sci. 26, No. 5 (1978), 407–413. (1978) MR0492684
- 164. S. Szufla, Sets of fixed points nonlinear mappings in function spaces, Funkcial. Ekvac. 22 (1979), 121–126. (1979) MR0551256
- 165. S. Szufla, On the existence of solutions of differential equations in Banach spaces, Bull. Acad. Polon. Sci. 30, No. 11–12 (1982), 507–515. (1982) MR0718727
- 166. S. Szufla, On the equation x = f (t, x) in locally convex spaces, Math. Nachr. 118 (1984), 179–185. (1984) MR0773619
- 167. S. Szufla, Existence theorems for solutions of integral equations in Banach spaces, Proc. Conf. Diff. Equs. and Optimal Control, Zielona Góra (1985), 101–107. (1985) MR0937926
- 168. S. Szufla, On the application of measure of noncompactness to differential and integral equations in a Banach space, Fasc. Math. 18 (1988), 5–11. (1988) MR0988763
- 169. P. Talaga, The Hukuhara–Kneser property for parabolic systems with nonlinear boundary conditions, J. Math. Anal. 79 (1981), 461–488. (1981) Zbl0457.35042MR0606494
- 170. P. Talaga, The Hukuhara–Kneser property for quasilinear parabolic equations, Non-linear Anal. TMA 12, No. 3 (1988), 231–245. (1988) Zbl0678.35052MR0928558
- 171. A. A. Tolstonogov, On differential inclusions in a Banach space and continuous selectors, Dokl. Akad. Nauk SSSR 244 (1979), 1088–1092. (1979) MR0522051
- 172. A. A. Tolstonogov, On properties of solutions of differential inclusions in a Banach space, Dokl. Akad. Nauk SSSR 248 (1979), 42–46. (1979) Zbl0441.34045MR0549368
- 173. A. A. Tolstonogov, On the structure of the solution set for differential inclusions in a Banach space, Math. Sbornik, 46 (1983), 1–15. (in Russian) (1983) Zbl0564.34065
- 174. G. Vidossich, On Peano-phenomenon, Bull. Un. Math. Ital. 3 (1970), 33–42. (1970) Zbl0179.47101MR0271793
- 175. G. Vidossich, On the structure of the set of solutions of nonlinear equations, J. Math. Anal. Appl. 34 (1971), 602–617. (1971) MR0283645
- 176. G. Vidossich, A fixed point theorem for function spaces, J. Math. Anal. Appl. 36 (1971), 581–587. (1971) MR0285945
- 177. G. Vidossich, Existence, uniqueness and approximation of fixed points as a generic property, Bol. Soc. Brasil. Mat. 5 (1974), 17–29. (1974) MR0397710
- 178. G. Vidossich, Two remarks on global solutions of ordinary differential equations in the real line, Proc. Amer. Math. Soc. 55 (1976), 111–115. (1976) Zbl0339.34004MR0470291
- 179. T. Wazewski, Sur l’existence et l’unicité des integrales des équations différentielles ordinaires au cas de l’espace de Banach, Bull. Acad. Polon. Math. 8 (1960), 301–305. (1960) Zbl0093.08405MR0131038
- 180. J. A. Yorke, Spaces of solutions, Lect. Notes Op. Res. Math. Econ. vol. 12, Springer-Verlag, (1969), 383–403. (1969) Zbl0188.15502MR0361294
- 181. J. A. Yorke, A continuous differential equation in a Hilbert space without existence, Funkc. Ekvac. 13 (1970), 19–21. (1970) MR0264196
- 182. R. R. Akhmerov, The structure of the solution set of a boundary value problem for a one-dimensional stationary equation of variable type, Chisl. Metody Mekh. Sploshn. Sredy, 15 (1984), 20–30. (1984) MR0813536
- 183. J. C. Alexander I. Massabò, J. Pejsachowicz, On the connectivity properties of the solution set of infinitely-parametrized families of vector fields, Boll. Un. Mat. Ital.A (6), 1 (1982), 309–312. (1982) MR0663297
- 184. A. Anguraj, K. Balachandran, On the solution sets of differential inclusion in Banach spaces, Tamkang J. Math., 23 (1992), 59–65. (1992) Zbl0760.34018MR1164448
- 185. G. Anichini, G. Conti, How to make use of the solution set to solve boundary value problems, Recent Trends in Nonlinear Analysis, Birkhäuser, Basel, 2000, 15–25. Zbl0949.34009MR1763129
- 186. G. Anichini G. Conti, P. Zecca, Using solution sets for solving boundary value problems for ordinary differential equations, Nonlinear Anal., 17 (1991), 465–472. (1991) MR1124119
- 187. M. T. Ashordiya, The structure of the solution set of the Cauchy problem for a system of generalized ordinary differential equations, Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy, 17 (1986), 5–16. (1986) MR0853272
- 188. E. P. Avgerinos, N. S. Papageorgiou, On the solution set of maximal monotone differential inclusions in , Math. Japon., 38 (1993), 91–110. (1993) MR1204188
- 189. E. P. Avgerinos, N. S. Papageorgiou, Topological properties of the solution set of integrodifferential inclusions, Comment. Math. Univ. Carolin., 36 (1995), 429–442. (1995) Zbl0836.34019MR1364483
- 190. G. Bartuzel, A. Fryszkowski, A topological property of the solution set to the Sturm–Liouville differential inclusions, Demonstratio Math., 28 (1995), 903–914. (1995) Zbl0886.47026MR1392243
- 191. J. W. Bebernes, Solution set properties for some nonlinear parabolic differential equations, Equadiff IV (Proc. Czechoslovak Conf. Differential Equations and their Applications, Prague, 1977) Springer, Berlin, 1979, 25–30. (1977) MR0535319
- 192. V. I. Blagodatskikh, P. Ndiĭ, Convexity of the solution set of a differential inclusion, Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., (1998), 21–22. (1998) MR1657954
- 193. F. S. De Blasi G. Pianigiani, V. Staicu, On the solution sets of some nonconvex hyperbolic differential inclusions, Czechoslovak Math. J., 45 (1995), 107–116. (1995) MR1314533
- 194. D. Bugajewska, On implicit Darboux problem in Banach spaces, Bull. Austral. Math. Soc., 56 (1997), 149–156. (1997) MR1464057
- 195. D. Bugajewska, On the equation of nth order and the Denjoy integral, Nonlinear Anal., 34 (1998), 1111–1115. (1998) MR1637221
- 196. D. Bugajewska, A note on the global solutions of the Cauchy problem in Banach spaces, Acta Math. Hung., 88 (2000), 341–346. MR1789046
- 197. D. Bugajewska, On the structure of solution sets of differential equations in Banach spaces, Math. Slovaca, 50 (2000), 463–471. MR1857301
- 198. D. Bugajewska, D. Bugajewski, On the equation , Czech. Math. Journal, 46 (1996), 325–330. (1996) MR1388620
- 199. D. Bugajewska, D. Bugajewski, On nonlinear equations in Banach spaces and axiomatic measures of noncompactness, Funct. Differ. Equ., 5 (1998), 57–68. (1998) Zbl1049.45013MR1681184
- 200. D. Bugajewski, On the structure of the -solution sets of Volterra integral equations in Banach spaces, Comment. Math. Prace Mat., 30 (1991), 253–260. (1991) Zbl0745.45004MR1122694
- 201. D. Bugajewski, On differential and integral equations in locally convex spaces, Demonstr. Math., 28 (1995), 961–966. (1995) Zbl0855.34071MR1392249
- 202. D. Bugajewski, On the structure of solution sets of differential and integral equations, and the Perron integral, Proceedings of the Prague Mathematical Conference 1996, Icaris, Prague, 1997, 47–51. (1996) Zbl0966.34041MR1703455
- 203. D. Bugajewski, S. Szufla, Kneser’s theorem for weak solutions of the Darboux problem in Banach spaces, Nonlinear Anal., 20 (1993), 169–173. (1993) MR1200387
- 204. D. Bugajewski, S. Szufla, On the Aronszajn property for differential equations and the Denjoy integral, Comment. Math., 35 (1995), 61–69. (1995) MR1384852
- 205. T. Cardinali, On the structure of the solution set of evolution inclusions with Fréchet subdifferentials, J. Appl. Math. Stochastic Anal., 13 (2000), 51–72. Zbl0966.34052MR1751029
- 206. T. Cardinali A. Fiacca, N. S. Papageorgiou, On the solution set of nonlinear integrodifferential inclusions in , Math. Japon., 46 (1997), 117–127. (1997) MR1466124
- 207. C. Castaing, M. Marques, Topological properties of solution sets for sweeping processes with delay, Portugal. Math., 54 (1997), 485–507. (1997) Zbl0895.34053MR1489988
- 208. A. Cellina, A. Ornelas, Convexity and the closure of the solution set to differential inclusions, Boll. Un. Mat. Ital. B (7), 4 (1990), 255–263. (1990) Zbl0719.34031MR1061215
- 209. R. M. Colombo A. Fryszkowski T. Rzezuchowski, V. Staicu, Continuous selections of solution sets of Lipschitzean differential inclusions, Funkcial. Ekvac., 34 (1991), 321–330. (1991) MR1130468
- 210. A. Constantin, On the stability of solution sets for operational differential inclusions, An. Univ. Timişoara Ser. Ştiinţ. Mat., 29 (1991), 115–124. (1991) Zbl0799.34016MR1263091
- 211. G. Conti V. Obukhovskiĭ, P. Zecca, On the topological structure of the solution set for a semilinear functional-differential inclusion in a Banach space, Topology in Nonlinear Analysis, Polish Acad. Sci., Warsaw, 1996, 159–169. (1996) MR1448435
- 212. K. Deimling, On solution sets of multivalued differential equations, Appl. Anal., 30 (1988), 129–135. (1988) Zbl0635.34014MR0967566
- 213. K. Deimling, Bounds for solution sets of multivalued ODEs, Recent Trends in Differential Equations, World Sci. Publishing, River Edge, NJ, 1992, 127–134. (1992) Zbl0832.34009MR1180107
- 214. P. Diamond, P. Watson, Regularity of solution sets for differential inclusions quasi-concave in a parameter, Appl. Math. Lett., 13 (2000), 31–35. Zbl0944.34008MR1750963
- 215. Y. H. Du, The structure of the solution set of a class of nonlinear eigenvalue problems, J. Math. Anal. Appl., 170 (1992), 567–580. (1992) Zbl0784.35080MR1188572
- 216. V. V. Filippov, On the acyclicity of solution sets of ordinary differential equations, Dokl. Akad. Nauk, 352 (1997), 28–31. (1997) MR1445851
- 217. A. Gavioli, On the solution set of the nonconvex sweeping process, Discuss. Math. Differential Incl., 19 (1999), 45–65. (1999) Zbl0954.34036MR1758498
- 218. V. V. Goncharov, Co-density and other properties of the solution set of differential inclusions with noncompact right-hand side, Discuss. Math. Differential Incl., 16 (1996), 103–120. (1996) Zbl0906.34012MR1646626
- 219. T. G. Hallam, J. W. Heidel, Structure of the solution set of some first order differential equations of comparison type, Trans. Amer. Math. Soc., 160 (1971), 501–512. (1971) MR0281995
- 220. G. Herzog, R. Lemmert, On the structure of the solution set of , , Math. Nachr., 215 (2000), 103–105. Zbl0953.34054MR1768196
- 221. S. C. Hu V. Lakshmikantham, N. S. Papageorgiou, On the solution set of nonlinear evolution inclusions, Dynamic Systems Appl., 1 (1992), 71–82. (1992) Zbl0755.34057MR1154650
- 222. S. C. Hu V. Lakshmikantham, N. S. Papageorgiou, On the properties of the solution set of semilinear evolution inclusions, Nonlinear Anal., 24 (1995), 1683–1712. (1995) Zbl0831.34014MR1330643
- 223. A. G. Ibrahim, A. M. Gomaa, Topological properties of the solution sets of some differential inclusions, Pure Math. Appl., 10 (1999), 197–223. (1999) Zbl0977.34008MR1742594
- 224. G. Isac, G. X.-Z. Yuan, Essential components and connectedness of solution set for complementarity problems, Fixed Point Theory and Applications (Chinju, 1998), Nova Sci. Publ., Huntington, NY, 2000, 35–46. (1998) MR1761212
- 225. N. A. Izobov, The measure of the solution set of a linear system with the largest lower exponent, Differentsial’nye Uravneniya, 24 (1988), 2168–2170, 2207. (1988) MR0982150
- 226. M. Kamenskiĭ V. Obukhovskiĭ, P. Zecca, Method of the solution sets for a quasilinear functional-differential inclusion in a Banach space, Differential Equations Dynam. Systems, 4 (1996), 339–350. (1996) MR1655630
- 227. R. Kannan, D. O’Regan, A note on the solution set of integral inclusions, J. Integral Equations Appl., 12 (2000), 85–94. MR1760899
- 228. Z. Kánnai, P. Tallos, Stability of solution sets of differential inclusions, Acta Sci. Math. (Szeged), 61 (1995), 197–207. (1995) MR1377359
- 229. M. Kisielewicz, Continuous dependence of solution sets for generalized differential equations of neutral type, Atti Accad. Sci. Istit. Bologna Cl. Sci. Fis. Rend. (13), 8 (1980/81), 191–195. (1980) MR0695193
- 230. M. Kisielewicz, Compactness and upper semicontinuity of solution set of generalized differential equation in a separable Banach space, Demonstratio Math., 15 (1982), 753–761. (1982) MR0693538
- 231. M. Kisielewicz, Properties of solution set of stochastic inclusions, J. Appl. Math. Stochastic Anal., 6 (1993), 217–235. (1993) Zbl0796.93106MR1238600
- 232. M. Kisielewicz, Quasi-retractive representation of solution sets to stochastic inclusions, J. Appl. Math. Stochastic Anal., 10 (1997), 227–238. (1997) Zbl1043.34505MR1468117
- 233. B. S. Klebanov, V. V. Filippov, On the acyclicity of the solution set of the Cauchy problem for differential equations, Mat. Zametki, 62 (1997). (1997) MR1635158
- 234. P. Korman, The global solution set for a class of semilinear problems, J. Math. Anal. Appl., 226 (1998), 101–120. (1998) Zbl0911.34016MR1646477
- 235. A. V. Lakeev, S. I. Noskov, Description of the solution set of a linear equation with an interval-defined operator and right-hand side, Dokl. Akad. Nauk, 330 (1993), 430–433. (1993) MR1241970
- 236. V. P. Maksimov, On the parametrization of the solution set of a functional-differential equation, Funct. Differ. Equ., Perm. Politekh. Inst., Perm, (1988), 14–21. (in Russian) (1988) MR1066717
- 237. V. P. Maksimov, On the parametrization of the solution set of a functional-differential equation, Funct. Differ. Equ., 3 (1996), 371–378. (1996) Zbl0881.34076MR1459318
- 238. A. Margheri, P. Zecca, Solution sets and boundary value problems in Banach spaces, Topol. Methods Nonlinear Anal., 2 (1993), 179–188. (1993) Zbl0799.34069MR1245485
- 239. A. Margheri, P. Zecca, Solution sets of multivalued Sturm–Liouville problems in Banach spaces, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 5 (1994), 161–166. (1994) Zbl0809.34026MR1292571
- 240. J. T. Markin, Stability of solution sets for generalized differential equations, J. Math. Anal. Appl., 46 (1974), 289–291. (1974) Zbl0293.34004MR0348218
- 241. M. Martelli, A. Vignoli, On the structure of the solution set of nonlinear equations, Nonlinear Anal., 7 (1983), 685–693. (1983) Zbl0519.47037MR0707077
- 242. I. Massabò, J. Pejsachowicz, On the connectivity properties of the solution set of parametrized families of compact vector fields, J. Funct. Anal., 59 (1984), 151–166. (1984) MR0766486
- 243. P. S. Milojević, On the index and the covering dimension of the solution set of semilinear equations, Nonlinear Functional Analysis and its Applications, Part 2 (Berkeley, Calif., 1983), Amer. Math. Soc., Providence, R.I., 1986, 183–205. (1983) MR0843608
- 244. P. S. Milojević, On the dimension and the index of the solution set of nonlinear equations, Trans. Amer. Math. Soc., 347 (1995), 835–856. (1995) MR1282894
- 245. O. Naselli, On the solution set of an equation of the type , Set-Valued Anal., 4 (1996), 399–405. (1996) Zbl0873.47041MR1422403
- 246. J. J. Nieto, On the structure of the solution set for first order differential equations, Appl. Math. Comput., 16 (1985), 177–187. (1985) MR0780794
- 247. J. J. Nieto, Structure of the solution set for semilinear elliptic equations, Differential Equations: Qualitative Theory, Vol. I, II (Szeged, 1984), North-Holland, Amsterdam, 1987, 799–807. (1984) MR0890578
- 248. W. Orlicz, S. Szufla, On the structure of -solution sets of integral equations in Banach spaces, Studia Math., 77 (1984), 465–477. (1984) MR0751767
- 249. V. G. Osmolovskiĭ, The local structure of the solution set of a first-order nonlinear boundary value problem with constraints at points, Sibirsk. Mat. Zh., 27 (1986), 140–154, 206. (1986) MR0873718
- 250. N. S. Papageorgiou, On the solution set of evolution inclusions driven by time dependent subdifferentials, Math. Japon., 37 (1992), 1087–1099. (1992) Zbl0810.34059MR1196384
- 251. F. Papalini, Properties of the solution set of evolution inclusions, Nonlinear Anal., 26 (1996), 1279–1292. (1996) Zbl0849.34017MR1376103
- 252. M. P. Pera, A topological method for solving nonlinear equations in Banach spaces and some related global results on the structure of the solution sets, Rend. Sem. Mat. Univ. Politec. Torino, 41 (1983), 9–30. (1983) Zbl0568.47038MR0778859
- 253. E. S. Polovinkin, The properties of continuity and differentiation of solution sets of Lipschitzean differential inclusions Modeling, Estimation and Control of Systems with Uncertainty (Sopron, 1990), Birkhäuser, Boston, 1991, 349–360. (1990) MR1132282
- 254. B. Ricceri, On the topological dimension of the solution set of a class of nonlinear equations, C. R. Acad. Sci. Paris Sér. I Math., 325 (1997), 65–70. (1997) Zbl0884.47043MR1461399
- 255. L. E. Rybiński, A fixed point approach in the study of the solution sets of Lipschitzian functional-differential inclusions, J. Math. Anal. Appl., 160 (1991), 24–46. (1991)
- 256. E. Serra M. Tarallo, S. Terracini, On the structure of the solution set of forced pendulum-type equations, J. Differ. Equ., 131 (1996), 189–208. (1996) MR1419011
- 257. A. Sghir, On the solution set of second-order delay differential inclusions in Banach spaces, Ann. Math. Blaise Pascal, 7 (2000), 65–79. Zbl0958.34048MR1769982
- 258. W. Song, The solution set of a differential inclusion on a closed set of a Banach space, Appl. Math., Warsaw, 23 (1995), 13–23. (1995) Zbl0831.34017MR1330055
- 259. W. Sosulski, Compactness and upper semicontinuity of solution set of functional-differential equations of hyperbolic type, Comment. Math. Prace Mat., 25 (1985), 359–362. (1985) Zbl0614.35061MR0844652
- 260. J. S. Spraker, D. C. Biles, A comparison of the Carathéodory and Filippov solution sets, J. Math. Anal. Appl., 198 (1996), 571–580. (198) MR1376281
- 261. V. Staicu, Continuous selections of solution sets to evolution equations, Proc. Amer. Math. Soc., 113 (1991), 403–413. (1991) Zbl0737.34011MR1076580
- 262. V. Staicu, On the solution sets to nonconvex differential inclusions of evolution type, Discrete Contin. Dynam. Systems, 2 (1998), 244–252. (1998) MR1722473
- 263. V. Staicu, H. Wu, Arcwise connectedness of solution sets to Lipschitzean differential inclusions, Boll. Un. Mat. Ital. A (7), 5 (1991), 253–256. (1991) Zbl0742.34018MR1120387
- 264. S. Szufla, Solutions sets of non-linear integral equations, Funkcial. Ekvac., 17 (1974), 67–71. (1974) MR0344827
- 265. S. Szufla, On the structure of solution sets of nonlinear equations, Differential Equations and Optimal Control (Kalsk, 1988), Higher College Engrg., Zielona Góra, 1989, 33–39. (1988) MR1067550
- 266. A. A. Tolstonogov, On the density and “being boundary” for the solution set of a differential inclusion in a Banach space, Dokl. Akad. Nauk SSSR, 261 (1981), 293–296. (1981) MR0638919
- 267. A. A. Tolstonogov, The solution set of a differential inclusion in a Banach space. II, Sibirsk. Mat. Zh., 25 (1984), 159–173. (1984) MR0732775
- 268. A. A. Tolstonogov, P. I. Chugunov, The solution set of a differential inclusion in a Banach space. I, Sibirsk. Mat. Zh., 24 (1983), 144–159. (1983) MR0731051
- 269. G. M. Troianiello, Structure of the solution set for a class of nonlinear parabolic problems, Nonlinear Parabolic Equations: Qualitative Properties of Solutions (Rome, 1985), Longman Sci. Tech., Harlow, 1987, 219–225. (1985) MR0901112
- 270. H. D. Tuan, On the continuous dependence on parameter of the solution set of differential inclusions, Z. Anal. Anwendungen, 11 (1992), 215–220. (1992) Zbl0783.34010MR1265929
- 271. Ya. I. Umanskiĭ, On a property of the solution set of differential inclusions in a Banach space, Differentsial’nye Uravneniya, 28 (1992), 1346–1351, 1468. (1992) MR1203847
- 272. V. Veliov, Convergence of the solution set of singularly perturbed differential inclusions, Proceedings of the Second World Congress of Nonlinear Analysts, Part 8 (Athens, 1996), Nonlinear Anal., 30 (1997), 5505–5514. (1996) MR1726055
- 273. Z. H. Wang, Existence of solutions for parabolic type evolution differential inclusions and the property of the solution set, Appl. Math. Mech., 20 (1999), 314–318. (1999) MR1704410
- 274. Z. K. Wei, On the existence of unbounded connected branches of solution sets of a class of semilinear operator equations, Bull. Soc. Math. Belg. Sér. B, 38 (1986), 14–30. (1986) MR0871300
- 275. Q. J. Zhu, On the solution set of differential inclusions in a Banach space, J. Differ. Equ., 93 (1991), 213–237. (1991) MR1125218
- 276. V. G. Zvyagin, The structure of the solution set of a nonlinear elliptic boundary value problem under fixed boundary conditions, Topological and Geometric Methods of Analysis, Voronezh. Gos. Univ., Voronezh, 1989, 152–158, 173. (in Russian) (1989) MR1047679
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