Second order multivalued boundary value problems

Nikolaos Halidias; Nikolaos S. Papageorgiou

Archivum Mathematicum (1998)

  • Volume: 034, Issue: 2, page 267-284
  • ISSN: 0044-8753

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Halidias, Nikolaos, and Papageorgiou, Nikolaos S.. "Second order multivalued boundary value problems." Archivum Mathematicum 034.2 (1998): 267-284. <http://eudml.org/doc/248205>.

@article{Halidias1998,
author = {Halidias, Nikolaos, Papageorgiou, Nikolaos S.},
journal = {Archivum Mathematicum},
keywords = {upper solution; lower solution; usc and lsc multifunction; Sturm-Liouville boundary conditions},
language = {eng},
number = {2},
pages = {267-284},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Second order multivalued boundary value problems},
url = {http://eudml.org/doc/248205},
volume = {034},
year = {1998},
}

TY - JOUR
AU - Halidias, Nikolaos
AU - Papageorgiou, Nikolaos S.
TI - Second order multivalued boundary value problems
JO - Archivum Mathematicum
PY - 1998
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 034
IS - 2
SP - 267
EP - 284
LA - eng
KW - upper solution; lower solution; usc and lsc multifunction; Sturm-Liouville boundary conditions
UR - http://eudml.org/doc/248205
ER -

References

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  1. Bernfeld S., Lakshmikantham V., An Introduction to Nonlinear Boundary Value Problems, Academic Press, New York (1974). (1974) Zbl0286.34018MR0445048
  2. Bressan A., Colombo G., Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), 69–85. (1988) Zbl0677.54013MR0947921
  3. Brezis H., Analyse Fonctionelle, Masson, Paris (1983). (1983) MR0697382
  4. Cabada A., Nieto J., Extremal solutions of second order nonlinear boundary value problems, Appl. Math. Comp. 40 (1990), 135–145. (1990) MR1080229
  5. Chang K. C., The obstacle problem and partial differential equations with discontinuous nonlinearities, Comm. Pure Appl. Math. 33 (1980), 117–146. (1980) Zbl0405.35074MR0562547
  6. DeBlasi F. S., Myjak J., On continuous approximations for multifunctions, Pacific J. Math. 123 (1986), 9–31. (1986) MR0834135
  7. Dunford N., Schwartz J., Linear Operators I, Wiley, New York (1958). (1958) 
  8. Erbe L., Krawcewicz W., Boundary value problems for differential inclusions y ' ' F t , y , y ' , Annales Polon Math. 56 (1990), 195–226. (1990) MR1114171
  9. Gaines R., Mawhin J., Coincidence Degree and Nonlinear Differential Equations, Springer Verlag, Berlin (1977). (1977) Zbl0339.47031MR0637067
  10. Gao W., Wang J., On nonlinear second order periodic boundary value problem with Caratheodory functions, Annales Polon Math. 62 (1995), 283–291. (1995) MR1356797
  11. Gilbarg D., Trudinger N., Elliptic Partial Differential Equations of Second Order, Springer Verlag, New York (1977). (1977) Zbl0361.35003MR0473443
  12. Himmelberg C., Fixed points of compact multifunctions, J. Math. Anal. Appl. 38 (1972). (1972) Zbl0225.54049MR0303368
  13. Kandilakis D., Papageorgiou N. S., Dirichlet and periodic problems for second order differential inclusions, Houston J. Math. – to appear. 
  14. Klein E., Thompson A., Theory of Correspondences, Wiley, New York (1984). (1984) Zbl0556.28012MR0752692
  15. Kravvaritis D., Papageorgiou N. S., Boundary value problems for nonconvex differential inclusions, J. Math. Anal. Appl. 185 (1994), 146–160. (1994) Zbl0817.34009MR1283047
  16. Leela S., Monotone method for second order periodic boundary value problems, Nonl. Anal. – TMA 7 (1983), 349–355. (1983) Zbl0524.34023MR0696734
  17. Marano S., Existence theorems for multivalued boundary value problems, Bull. Austr. Math. Soc. 45 (1992), 249–260. (1992) MR1155483
  18. Mönch H., Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonl. Anal. – TMA 4 (1980), 985–999. (1980) MR0586861
  19. Nieto J., Nonlinear second order periodic value problems with Caratheodory functions, Appl. Anal. 34 (1989), 111–128. (1989) 
  20. Nieto J., Cabada A., A generalized upper and lower solutions method for nonlinear second order ordinary differential equations, J. Appl. Math. Stoch. Anal. 5 (1992), 157–166. (1992) Zbl0817.34016MR1214298
  21. Nkashama M. N., A generalized upper and lower solutions method and multiplicity results for nonlinear first–order ordinary differential equations, J. Math. Anal. Appl. 140 (1989), 381–395. (1989) Zbl0674.34009MR1001864
  22. Omari P., A monotone method for constructing extremal solutions of second order scalar boundary value problems, Appl. Math. Comp. 18 (1986), 257–275. (1986) Zbl0625.65075MR0827837
  23. Omari P., Trombetta M., Remarks on the lower and upper solutions method for second and third order periodic boundary value problems, Appl. Math. Comp. 50 (1992), 1–21. (1992) Zbl0760.65078MR1164490
  24. Papageorgiou N. S., Convergence theorems for Banach space valued integrable multifunctions, Intern. J. Math.. Sci. 10 10 (1987), 433–442. (1987) Zbl0619.28009MR0896595
  25. Papageorgiou N. S., On measurable multifunctions with applications to multivalued equations, Math. Japonica 32 (1987), 437–464. (1987) MR0914749
  26. Papageorgiou N. S., Decomposable sets in the Lebesgue–Bochner spaces, Comm. Math. Univ. Sancti Pauli 37 (1988), pp. 49–62. (1988) Zbl0679.46032MR0942305
  27. Papageorgiou N. S., Papalini F., Periodic and boundary value problems for second order differential equations, Trans. AMS – to appear. Zbl0986.34011MR1818423
  28. Vrabie I., Compactness Methods for Nonlinear Evolutions, Longman Scientific and Technical, Essex, U.K. (1987). (1987) Zbl0721.47050MR0932730
  29. Wagner D., Survey of measurable selection theorems, SIAM J. Control Optim. 15 (1977), 859–903. (1977) Zbl0407.28006MR0486391

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