On a class of quasilinear elliptic problems involving Trudinger-Moser nonlinearities

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:403

Article

de Souza, Manasses¹  de Medeiros, Everaldo¹  Severo, Uberlandio¹ 

[1] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba, Brazil

关键词: Leray-Lions operator;    Trudinger-Moser inequality;    Fixed point theorem;    Discontinuous nonlinearity;   

DOI  :  10.1016/j.jmaa.2013.01.064

来源: Elsevier

【 摘 要 】

In this paper we consider the following class of quasilinear elliptic problems: -div(a(x, del u)) = lambda h(x) exp(alpha(0)vertical bar u vertical bar(n/n-1)) + f(x, u) in Omega, with the Dirichlet boundary condition where Omega subset of R-n (n >= 2) is a smooth bounded domain and lambda > 0 is a positive parameter. We assume that there exists A : Omega x R-n -> R such that a = del A satisfies some mild conditions, h(x) and f (x, s) are mensurable functions and f (x, s) can enjoy exponential critical growth. The approach relies on a fixed point theorem and the Trudinger-Moser inequality. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free