Periodic parabolic problems with nonlinearities indefinite in sign
Godoy, T. (Universidad Nacional de Córdoba (Argentina). Facultad de Matemática, Astronomía y Física)
Kaufmann, U. (Universidad Nacional de Córdoba (Argentina). Facultad de Matemática, Astronomía y Física)

Date:	2007
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) u p − b (x, t) u q 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.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Published in:	Publicacions matemàtiques, V. 51 n. 1 (2007) p. 45-57, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/218482
DOI: 10.5565/PUBLMAT_51107_03

13 p, 177.4 KB

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