| 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 |
| DOI:
|
10.21136/AM.1979.103807 |
| . |
| Date available:
|
2008-05-20T18:12:18Z |
| Last updated:
|
2020-07-28 |
| 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Unpublished Lecture Notes, Dept.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). |
| . |
