Existence and regularity to an elliptic equation with logarithmic nonlinearity

Autor(es)

Montenegro, Marcelo ^[1] ; de Queiroz, Olivaine Santana ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Matemat, IMECC, BR-13083970 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 246, n. 2, p. 482-511, JAN 15 2009.
• Citações Web of Science: 9

Resumo

We study the nonlinear elliptic problem -Delta u = X([u>0])(log u + lambda f (x,u)) in Omega subset of R(n) with u = 0 on partial derivative Omega. The function f : Omega x {[}0, infinity) -> {[}0,infinity) is nondecreasing, sublinear and f(u) is continuous. For every lambda > 0, we obtain a maximal solution u(lambda) >= 0 and prove its global regularity C(1.gamma) ((Omega) over bar). There is a constant lambda{*} such that u(lambda) vanishes on a set of positive measure for 0 < lambda <{*}, and u(lambda) > 0 for lambda >lambda{*}. If f is concave, for), lambda > lambda{*} we characterize u(lambda) by its stability. (C) 2008 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 04/04651-7 - Equacoes elipticas e parabolicas singulares .
• Beneficiário: Olivâine Santana de Queiroz
• Modalidade de apoio: Bolsas no Brasil - Doutorado