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
@article{10_21136_AM_1979_103807,
author = {\v{S}\v{t}astnov\'a, V\v{e}nceslava and Fu\v{c}{\'\i}k, Svatopluk},
title = {Weak periodic solutions of the boundary value problem for nonlinear heat equation},
journal = {Applications of Mathematics},
pages = {284--303},
year = {1979},
volume = {24},
number = {4},
doi = {10.21136/AM.1979.103807},
mrnumber = {0533778},
zbl = {0429.35039},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1979.103807/}
}
TY - JOUR AU - Šťastnová, Věnceslava AU - Fučík, Svatopluk TI - Weak periodic solutions of the boundary value problem for nonlinear heat equation JO - Applications of Mathematics PY - 1979 SP - 284 EP - 303 VL - 24 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.21136/AM.1979.103807/ DO - 10.21136/AM.1979.103807 LA - en ID - 10_21136_AM_1979_103807 ER -
%0 Journal Article %A Šťastnová, Věnceslava %A Fučík, Svatopluk %T Weak periodic solutions of the boundary value problem for nonlinear heat equation %J Applications of Mathematics %D 1979 %P 284-303 %V 24 %N 4 %U http://geodesic.mathdoc.fr/articles/10.21136/AM.1979.103807/ %R 10.21136/AM.1979.103807 %G en %F 10_21136_AM_1979_103807
Šťastnová, Věnceslava; Fučík, Svatopluk. Weak periodic solutions of the boundary value problem for nonlinear heat equation. Applications of Mathematics, Tome 24 (1979) no. 4, pp. 284-303. doi: 10.21136/AM.1979.103807
[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
[2] E. N. Dancer: On the Dirichlet problem for weakly nonlinear partial differential equations. (to appear).
[3] P. Drábek: Graduate thesis, MFF UK 1977 (to be published).
[4] S. Fučík: Nonlinear equations with noninvertible linear part. Czechoslovak Math. J. 24 (99), 1974, 259-271. | MR
[5] S. Fučík: Boundary value problems with jumping nonlinearities. Čas. Pěstování Mat. 101 (1976), 69-87. | MR
[6] S. Fučík: Solvability and nonsolvability of weakly nonlinear equations. Proc. Int. Summer School „Theory on Nonlinear Operators", Berlin (GDR), September 22-26, 1975.
[7] S. Fučík: Remarks on some nonlinear boundary value problems. Comment. Math. Univ. Carolinae 17 (1976), 721-730. | MR
[8] S. Fučík: Ranges of Nonlinear Operators. Unpublished Lecture Notes, Dept. Math. Anal., Charles University, 1977.
[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. | DOI | MR
[10] S. Fučík J. Nečas J. Souček V. Souček: Spectral Analysis of Nonlinear Operators. Lecture Notes in Mathematics No 346. Springer-Verlag, 1973. | MR
[11] S. Fučík J. Nečas V. Souček: Einführung in die Variationsrechnung. Teubner Texte zur Mathematik. Teubner, Leipzig, 1977. | MR
[12] R. E. Gaines J. L. Mawhin: Coincidence degree, and nonlinear differential equations. Lecture Notes in Mathematics No 568. Springer-Verlag 1977. | MR
[13] M. Konečný: Remarks on periodic solvability of nonlinear ordinary differential equations. Comment. Math. Univ. Carolinae 18 (1977), 547-562. | MR
[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
[15] О. В. Бесов В.П. Ильин С. M. Никольский: Интегральные представления функций и теоремы вложения. Изд. ,,Наука", Москва 1975. | Zbl
[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.
[17] O. Vejvoda, Соmр.: Partial differential equations-periodic solutions. (manuscript of a prepared book).
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