Boundary Value Problems 
Volume 2006 (2006), Article ID 41295, 17 pages
doi:10.1155/BVP/2006/41295

Existence and multiplicity of weak solutions for a class of degenerate nonlinear elliptic equations

Mihai Mihăilescu

 Department of Mathematics, University of Craiova, Craiova 200 585, Romania
Received 11 January 2005; Revised 4 July 2005; Accepted 17 July 2005

Abstract

The goal of this paper is to study the existence and the multiplicity of non-trivial weak solutions for some degenerate nonlinear elliptic equations on the whole space RN. The solutions will be obtained in a subspace of the Sobolev space W1/p(RN). The proofs rely essentially on the Mountain Pass theorem and on Ekeland's Variational principle.