Previous |  Up |  Next

Article

Title: Weak periodic solutions of the boundary value problem for nonlinear heat equation (English)
Author: Šťastnová, Věnceslava
Author: Fučík, Svatopluk
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 24
Issue: 4
Year: 1979
Pages: 284-303
Summary lang: English
Summary lang: Czech
Summary lang: Russian
.
Category: math
.
Summary: 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. (English)
Keyword: periodic solution
Keyword: nonlinear heat equation
Keyword: bounded, vanishing and jumping nonlinearities
Keyword: weak solution
Keyword: singular case
Keyword: solvability of Landesman-Lazer type
Keyword: Schauder fixed point theorem
Keyword: ordinary differential equation
MSC: 35A25
MSC: 35B10
MSC: 35K05
MSC: 35K55
MSC: 35K60
idZBL: Zbl 0429.35039
idMR: MR0533778
.
Date available: 2008-05-20T18:12:18Z
Last updated: 2015-07-13
Stable URL: http://hdl.handle.net/10338.dmlcz/103807
.
Reference: [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). MR 0513090
Reference: [2] E. N. Dancer: On the Dirichlet problem for weakly nonlinear partial differential equations.(to appear).
Reference: [3] P. Drábek: .Graduate thesis, MFF UK 1977 (to be published).
Reference: [4] S. Fučík: Nonlinear equations with noninvertible linear part.Czechoslovak Math. J. 24 (99), 1974, 259-271. MR 0348568
Reference: [5] S. Fučík: Boundary value problems with jumping nonlinearities.Čas. Pěstování Mat. 101 (1976), 69-87. MR 0447688
Reference: [6] S. Fučík: Solvability and nonsolvability of weakly nonlinear equations.Proc. Int. Summer School „Theory on Nonlinear Operators", Berlin (GDR), September 22-26, 1975.
Reference: [7] S. Fučík: Remarks on some nonlinear boundary value problems.Comment. Math. Univ. Carolinae 17 (1976), 721-730. MR 0427724
Reference: [8] S. Fučík: Ranges of Nonlinear Operators.Unpublished Lecture Notes, Dept. Math. Anal., Charles University, 1977.
Reference: [9] S. Fučík M. Krbec: Boundary value problems with bounded nonlinearities and general null-space of the linear part.Math. Z. 155 (1977), 129-138. MR 0473513, 10.1007/BF01214212
Reference: [10] S. Fučík J. Nečas J. Souček V. Souček: Spectral Analysis of Nonlinear Operators.Lecture Notes in Mathematics No 346. Springer-Verlag, 1973. MR 0467421
Reference: [11] S. Fučík J. Nečas V. Souček: Einführung in die Variationsrechnung.Teubner Texte zur Mathematik. Teubner, Leipzig, 1977. MR 0487654
Reference: [12] R. E. Gaines J. L. Mawhin: Coincidence degree, and nonlinear differential equations.Lecture Notes in Mathematics No 568. Springer-Verlag 1977. MR 0637067
Reference: [13] M. Konečný: Remarks on periodic solvability of nonlinear ordinary differential equations.Comment. Math. Univ. Carolinae 18 (1977), 547-562. MR 0470340
Reference: [14] E. M. Landesman A. C. Lazer: Nonlinear perturbations of linear elliptic boundary value problems at resonance.J. Math. Mech. 19, 1970, 609-623. MR 0267269
Reference: [15] О. В. Бесов В.П. Ильин С. M. Никольский: Интегральные представления функций и теоремы вложения.Изд. ,,Наука", Москва 1975. Zbl 1231.90252
Reference: [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.
Reference: [17] O. Vejvoda, Соmр.: Partial differential equations-periodic solutions.(manuscript of a prepared book).
.

Files

Files Size Format View
AplMat_24-1979-4_5.pdf 2.829Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo