Boundary Value Problems
Volume 2006 (2006), Article ID 41295, 17 pages

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

Copyright © 2006 Mihai Mihăilescu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.