# Periodic parabolic problems with nonlinearities indefinite in sign.

Publicacions Matemàtiques (2007)

- Volume: 51, Issue: 1, page 45-57
- ISSN: 0214-1493

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topGodoy, Tomás, and Kaufmann, Uriel. "Periodic parabolic problems with nonlinearities indefinite in sign.." Publicacions Matemàtiques 51.1 (2007): 45-57. <http://eudml.org/doc/41886>.

@article{Godoy2007,

abstract = {Let Ω ⊂ RN be a smooth bounded domain. We give sufficient conditions (which are also necessary in many cases) on two nonnegative functions a, b that are possibly discontinuous and unbounded for the existence of nonnegative solutions for semilinear Dirichlet periodic parabolic problems of the form Lu = λa (x, t) up - b (x, t) uq in Ω × R, where 0 < p, q < 1 and λ > 0. In some cases we also show the existence of solutions uλ in the interior of the positive cone and that uλ can be chosen such that λ → uλ is differentiable and increasing. A uniqueness theorem is also given in the case p ≤ q. All results remain valid for the corresponding elliptic problems.},

author = {Godoy, Tomás, Kaufmann, Uriel},

journal = {Publicacions Matemàtiques},

keywords = {Ecuaciones parabólicas; Problemas de valor de frontera; Problema de Dirichlet; Teorema de existencia; periodic nonnegative solution; indefinite nonlinearity; semilinear Dirichlet periodic parabolic problems},

language = {eng},

number = {1},

pages = {45-57},

title = {Periodic parabolic problems with nonlinearities indefinite in sign.},

url = {http://eudml.org/doc/41886},

volume = {51},

year = {2007},

}

TY - JOUR

AU - Godoy, Tomás

AU - Kaufmann, Uriel

TI - Periodic parabolic problems with nonlinearities indefinite in sign.

JO - Publicacions Matemàtiques

PY - 2007

VL - 51

IS - 1

SP - 45

EP - 57

AB - Let Ω ⊂ RN be a smooth bounded domain. We give sufficient conditions (which are also necessary in many cases) on two nonnegative functions a, b that are possibly discontinuous and unbounded for the existence of nonnegative solutions for semilinear Dirichlet periodic parabolic problems of the form Lu = λa (x, t) up - b (x, t) uq in Ω × R, where 0 < p, q < 1 and λ > 0. In some cases we also show the existence of solutions uλ in the interior of the positive cone and that uλ can be chosen such that λ → uλ is differentiable and increasing. A uniqueness theorem is also given in the case p ≤ q. All results remain valid for the corresponding elliptic problems.

LA - eng

KW - Ecuaciones parabólicas; Problemas de valor de frontera; Problema de Dirichlet; Teorema de existencia; periodic nonnegative solution; indefinite nonlinearity; semilinear Dirichlet periodic parabolic problems

UR - http://eudml.org/doc/41886

ER -