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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)

Data: 2007
Resum: 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.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Publicat a: Publicacions Matemàtiques, V. 51 n. 1 (2007) p. 45-57, ISSN 0214-1493

Adreça original:
DOI: 10.5565/PUBLMAT_51107_03
DOI: 10.5565/218482

13 p, 177.4 KB

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