Existence and multiplicity of solutions for a class of quasilinear elliptic equations: An Orlicz-Sobolev space setting

摘要

In this paper, we study the existence and multiplicity of solutions of the following quasilinear elliptic problem {-div(a(vertical bar del u vertical bar)del u) = f(x, u), in Omega, u = 0, on partial derivative Omega, where Omega subset of R-N is a bounded domain with smooth boundary partial derivative Omega. The existence and multiplicity of solutions are obtained by genus theory, symmetric mountain pass lemma, fountain theorem and dual fountain theorem, respectively. (C) 2011 Elsevier Inc. All rights reserved.