Periodic parabolic problems with nonlinearities indefinite in sign.

Godoy, 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 &lt; p, q &lt; 1 and λ &gt; 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 &lt; p, q &lt; 1 and λ &gt; 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 -