Existence and regularity to an elliptic equation with logarithmic nonlinearity

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:246

Article

Montenegro, Marcelo¹  de Queiroz, Olivaine Santana¹ 

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

关键词: Regularity;    Singular problem;    Elliptic equation;   

DOI  :  10.1016/j.jde.2008.06.035

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free