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

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.