%0 Journal Article %T Existence and multiplicity of weak solutions for a class of degenerate nonlinear elliptic equations %A Mih£¿ilescu Mihai %J Boundary Value Problems %D 2006 %I Springer %X 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 . The solutions will be obtained in a subspace of the Sobolev space . The proofs rely essentially on the Mountain Pass theorem and on Ekeland's Variational principle. %U http://www.boundaryvalueproblems.com/content/2006/41295