On a singular and nonhomogeneous N-Laplacian equation involving critical growth

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:380

Article

de Souza, Manasses²  do O, Joao Marcos¹ 

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

[2] Univ Fed Pernambuco, Dept Matemat, BR-50740540 Recife, PE, Brazil

关键词: Variational methods;    Quasilinear elliptic equations;    Trudinger-Moser inequality;    Critical points;    Critical exponents;   

DOI  :  10.1016/j.jmaa.2011.03.028

来源: Elsevier

【 摘 要 】

In this paper we apply minimax methods to obtain existence and multiplicity of weak solutions for singular and nonhomogeneous elliptic equation of the form -Delta(N)u = f(x, u)/|x|a + h(x) in Omega, where u epsilon W-0(1,N)(Omega), Delta(N)u =diV(|del u|(N-2 del)u) is the N-Laplacian, a epsilon [0, N), Omega is a smooth bounded domain in R-N (N >= 2) containing the origin and h epsilon (W-0(1,N)(Omega))* = W--1,W-N' is a small perturbation, h not equivalent to 0. Motivated by a singular Trudinger-Moser inequality, we study the case when f (x, s) has the maximal growth on s which allows to treat this problem variationally in the Sobolev space W-0(1,N)(Omega). (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free