A topological structure of solution sets to evolution systems

Vladimír Ďurikovič; Monika Ďurikovičová

Mathematica Slovaca (2005)

  • Volume: 55, Issue: 5, page 529-554
  • ISSN: 0232-0525

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Ďurikovič, Vladimír, and Ďurikovičová, Monika. "A topological structure of solution sets to evolution systems." Mathematica Slovaca 55.5 (2005): 529-554. <http://eudml.org/doc/34616>.

@article{Ďurikovič2005,
author = {Ďurikovič, Vladimír, Ďurikovičová, Monika},
journal = {Mathematica Slovaca},
keywords = {evolution system; initial-boundary value problem; linear Fredholm operator; proper and coercive operator; bifurcation point; surjectivity},
language = {eng},
number = {5},
pages = {529-554},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {A topological structure of solution sets to evolution systems},
url = {http://eudml.org/doc/34616},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Ďurikovič, Vladimír
AU - Ďurikovičová, Monika
TI - A topological structure of solution sets to evolution systems
JO - Mathematica Slovaca
PY - 2005
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 55
IS - 5
SP - 529
EP - 554
LA - eng
KW - evolution system; initial-boundary value problem; linear Fredholm operator; proper and coercive operator; bifurcation point; surjectivity
UR - http://eudml.org/doc/34616
ER -

References

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  1. AGRANOVIC M. S.-VISIK M. I., Eliptic problems with a parameter and parabolic general type problems, Uspekhi Mat. Nauk 19 (1964), 53-161. (Russian) (1964) MR0192188
  2. AMBROSETTI A., Global inversion theorems and applications to nonlinear problems, Conf. Semin. Mat. Univ. Bari 163-168 (1979), 211-232. (1979) Zbl0449.35041MR0585116
  3. ANDRES J.-GABOR G.-GORNIEWICZ L., Boundary value problems on infinite intervals, Trans. Amer. Math. Soc 351 (2000), 4861-4903. Zbl0936.34023MR1603870
  4. ANDRES J.-GABOR G.-GORNIEWICZ L., Topological structure of solution sets to multi-valued asymptotic problems, Z. Anal. Anwendungen 19 (2000), 35-60. Zbl0974.34045MR1748055
  5. ARONSZAJN N., Le correspondant topologique de Vunicite dans la theorie des equations differentielles, Ann. of Math. (2) 43 (1942), 730-738. (1942) MR0007195
  6. BANACH S.-MAZUR S., Über mehrdeutige stetige Abbildungen, Studia Math. 5 (1934), 174-178. (1934) Zbl0013.08202
  7. BORISOVIC, JU. G.-ZVJAGIN V. G.-SAPRONOV, JU. G., Nonlinear Fredholm mappings and the Leray-Schauder theory, Uspekhi Mat. Nauk 32 (1977), 3-54. (Russian) (1977) MR0464282
  8. BROWDER F. E.-GUPTA, CH. P., Topological degree and nonlinear mappings of analytic type in Banach spaces, J. Math. Anal. Appl. 26 (1969), 390-402. (1969) Zbl0176.45401MR0257826
  9. CACCIOPOLI R., Un principio di inversione per le corrispondenze funzionali e sue applicazioni alle equazioni alle derivate parziali, Rend. Accad. Naz. Lincei 6(16) (1932). (1932) 
  10. DEIMLING K., Nonlinear Functional Analysis, Springer-Verlag, Berlin-Heidelberg, 1985. (1985) Zbl0559.47040MR0787404
  11. DURIKOVIC V., An initial-boundary value problem for quasi-linear parabolic systems of higher order, Ann. Polon. Math. 30 (1974), 145-164. (1974) Zbl0249.35048MR0350206
  12. DURIKOVIC V.-DURIKOVICOVA, MA., Some generic properties of nonlinear second order diffusional type problem, Arch. Math. (Brno) 35 (1999), 229-244. (1999) Zbl1046.35016MR1725840
  13. DURIKOVIC V.-DURIKOVICOVA, MO., Sets of solutions of nonlinear initial-boundary value problems, Topol. Methods Nonlinear Anal. 17 (2001), 157-182. Zbl1066.35011MR1846985
  14. EIDEL'MAN S. D., Parabolic Systems, Nauka, Moskva, 1964. (Russian) (1964) Zbl0148.34604MR0167726
  15. EIDEL'MAN S. D.-IVASISEN S. D., The investigation of the Green's matrix for homogeneous boundary value problems of a parabolic type, Tr. Mosk. Mat. Obs. 23 (1970), 179-234. (Russian) (1970) MR0367455
  16. FUJITA H., On some nonexistence and nonuniqueness theorems for nonlinear parabolic equation, In: Nonlinear Functional Analysis. Proc Sympos. Pure Math. 18, Part 1, Chicago 1968, Amer. Math. Soc, Providence, RJ, 1970, pp. 105-113. (1968) MR0269995
  17. GORNIEWICZ L., Topological Fixed Point Theory of Multivalued Mappings, Math. Appl. 495, Kluwer Academic Publishers, Dordrecht-Boston-London, 1999. (1999) Zbl0937.55001MR1748378
  18. HENRY D., Geometric Theory of Semilinear Parabolic Equations, Springer-Verlag, Berlin-Heidelberg-New York, 1981. (1981) Zbl0456.35001MR0610244
  19. IVASISEN S. D., Green Matrices of Parabolic Boundary Value Problems, Vyshsha Shkola, Kijev, 1990. (Russian) (1990) 
  20. MARTELI M.-VIGNOLI A., A generalized Leray-Schauder condition, Rend. Accad. Naz. Lincei 57 (1974), 374-379. (1974) MR0417870
  21. MARTIN R. H., Nonlinear Operator and Differential Equations in Banach Spaces, Yohn Villey and Sons, New York-London-Sydney-Toronto, 1975. (1975) 
  22. QUINN F., Transversal approximation on Banach manifolds, In: Global Analysis. Proc. Sympos. Pure Math. 15, Amer. Math. Soc, Providence, RI, 1970, pp. 213-223. (1970) Zbl0206.25705MR0264713
  23. SADYRCHANOV R. S., Selected Questions of Nonlinear Functional Analysis, Publishers ELM, Baku, 1989. (Russian) (1989) 
  24. SMALE S., An infinite dimensional version of Sard's theorem, Amer. J. Math. 87 (1965), 861-866. (1965) Zbl0143.35301MR0185604
  25. SOLONIKOV V. A., Estimations of L solutions for elliptic and parabolic systems, Tr. Math. Inst. Steklova 102 (1969), 446-472. (1969) 
  26. SOLONIKOV V. A., On Boundary value problem for linear parabolic differential systems of the general type, Tr. Math. Inst. Steklova 83 (1965), 3-162. (Russian) (1965) 
  27. SEDA V., Fredholm mappings and the generalized boundary value problem, Differential Integral Equations 8 (1995), 19-40. (1995) Zbl0818.34014MR1296108
  28. TAYLOR A. E., Introduction of Functional Analysis, John Wiley and Sons, Inc., New York, 1967. (1967) MR0098966
  29. TRENOGIN V. A., Functional Analysis, Nauka, Moscow, 1980. (Russian) (1980) Zbl0517.46001MR0598629
  30. YOSIDA K., Functional Analysis, Springer-Verlag, Berlin-Heidelberg-New York, 1966. (1966) 
  31. ZEIDLER E., Nonlinear Functional Analysis and its Applications I, Fixed-Point Theorems, Springer-Verlag, Berlin-Heidelberg-Tokyo, 1986. (1986) Zbl0583.47050MR0816732
  32. ZEIDLER E., Nonlinear Functional Analysis and its Applications II/B, Nonlinear Monotone Operators, Springer-Verlag, Berlin-Heidelberg-London-Paris-Tokyo, 1990. (1990) Zbl0684.47029MR1033498

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