Weak periodic solutions of the boundary value problem for nonlinear heat equation

Věnceslava Šťastnová; Svatopluk Fučík

Aplikace matematiky (1979)

  • Volume: 24, Issue: 4, page 284-303
  • ISSN: 0862-7940

Abstract

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The paper deals with the existence of periodic solutions of the boundary value problem for nonlinear heat equation, where various types of nonlinearities are considered. The proofs are based on the investigation of Liapunov-Schmidt bifurcation system via Leray-Schauder degree theory.

How to cite

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Šťastnová, Věnceslava, and Fučík, Svatopluk. "Weak periodic solutions of the boundary value problem for nonlinear heat equation." Aplikace matematiky 24.4 (1979): 284-303. <http://eudml.org/doc/15104>.

@article{Šťastnová1979,
abstract = {The paper deals with the existence of periodic solutions of the boundary value problem for nonlinear heat equation, where various types of nonlinearities are considered. The proofs are based on the investigation of Liapunov-Schmidt bifurcation system via Leray-Schauder degree theory.},
author = {Šťastnová, Věnceslava, Fučík, Svatopluk},
journal = {Aplikace matematiky},
keywords = {periodic solution; nonlinear heat equation; bounded; vanishing and jumping nonlinearities; weak solution; singular case; solvability of Landesman-Lazer type; Schauder fixed point theorem; ordinary differential equation; periodic solution; nonlinear heat equation; bounded, vanishing and jumping nonlinearities; weak solution; singular case; solvability of Landesman-Lazer type; Schauder fixed point theorem; ordinary differential equation},
language = {eng},
number = {4},
pages = {284-303},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weak periodic solutions of the boundary value problem for nonlinear heat equation},
url = {http://eudml.org/doc/15104},
volume = {24},
year = {1979},
}

TY - JOUR
AU - Šťastnová, Věnceslava
AU - Fučík, Svatopluk
TI - Weak periodic solutions of the boundary value problem for nonlinear heat equation
JO - Aplikace matematiky
PY - 1979
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 24
IS - 4
SP - 284
EP - 303
AB - The paper deals with the existence of periodic solutions of the boundary value problem for nonlinear heat equation, where various types of nonlinearities are considered. The proofs are based on the investigation of Liapunov-Schmidt bifurcation system via Leray-Schauder degree theory.
LA - eng
KW - periodic solution; nonlinear heat equation; bounded; vanishing and jumping nonlinearities; weak solution; singular case; solvability of Landesman-Lazer type; Schauder fixed point theorem; ordinary differential equation; periodic solution; nonlinear heat equation; bounded, vanishing and jumping nonlinearities; weak solution; singular case; solvability of Landesman-Lazer type; Schauder fixed point theorem; ordinary differential equation
UR - http://eudml.org/doc/15104
ER -

References

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  1. H. Brézis L. Nirenberg, Characterizations of the ranges of some nonlinear operators and applications to boundary value problems, Ann. Scuola Norm. Sup. Pisa (to appear). Zbl0386.47035MR0513090
  2. E. N. Dancer, On the Dirichlet problem for weakly nonlinear partial differential equations, (to appear). Zbl0466.35038
  3. P. Drábek, [unknown], Graduate thesis, MFF UK 1977 (to be published). (1977) 
  4. S. Fučík, Nonlinear equations with noninvertible linear part, Czechoslovak Math. J. 24 (99), 1974, 259-271. (1974) Zbl0315.47038MR0348568
  5. S. Fučík, Boundary value problems with jumping nonlinearities, Čas. Pěstování Mat. 101 (1976), 69-87. (1976) Zbl0332.34016MR0447688
  6. S. Fučík, Solvability and nonsolvability of weakly nonlinear equations, Proc. Int. Summer School „Theory on Nonlinear Operators", Berlin (GDR), September 22-26, 1975. (1975) Zbl0334.47042
  7. S. Fučík, Remarks on some nonlinear boundary value problems, Comment. Math. Univ. Carolinae 17 (1976), 721-730. (1976) Zbl0353.34023MR0427724
  8. S. Fučík, Ranges of Nonlinear Operators, Unpublished Lecture Notes, Dept. Math. Anal., Charles University, 1977. (1977) Zbl0366.47027
  9. S. Fučík M. Krbec, 10.1007/BF01214212, Math. Z. 155 (1977), 129-138. (1977) Zbl0337.35034MR0473513DOI10.1007/BF01214212
  10. S. Fučík J. Nečas J. Souček V. Souček, Spectral Analysis of Nonlinear Operators, Lecture Notes in Mathematics No 346. Springer-Verlag, 1973. (1973) Zbl0268.47056MR0467421
  11. S. Fučík J. Nečas V. Souček, Einführung in die Variationsrechnung, Teubner Texte zur Mathematik. Teubner, Leipzig, 1977. (1977) Zbl0384.49001MR0487654
  12. R. E. Gaines J. L. Mawhin, Coincidence degree, and nonlinear differential equations, Lecture Notes in Mathematics No 568. Springer-Verlag 1977. (1977) Zbl0339.47031MR0637067
  13. M. Konečný, Remarks on periodic solvability of nonlinear ordinary differential equations, Comment. Math. Univ. Carolinae 18 (1977), 547-562. (1977) Zbl0371.34026MR0470340
  14. E. M. Landesman A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19, 1970, 609-623. (1970) Zbl0193.39203MR0267269
  15. О. В. Бесов В.П. Ильин С. M. Никольский, Интегральные представления функций и теоремы вложения, Изд. ,,Наука", Москва 1975. (1975) Zbl1231.90252
  16. V. Šťastnová О. Vejvoda, Periodic solutions of the first boundary value problem for linear and weakly nonlinear heat equation, Apl. Mat. 13 (1968), 466-477; 14 (1969), 241. (1968) Zbl0165.44302
  17. O. Vejvoda, Соmр., Partial differential equations-periodic solutions, (manuscript of a prepared book). 

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