Multiplicity of solutions for a class of nonlinear nonhomogeneous elliptic equations

Abstract

We consider nonlinear, nonhomogeneous Dirichlet problems driven by the sum of a p−Laplacian (p > 2) and a Laplacian, with a reaction term which has space dependent zeros of constant sign. We prove three muliplicity theorems for such equations providing precise sign information for all solutions. In the first multiplicity theorem, we do not impose any growth condition on the reaction near ±∞: In the other two, we assume that the reaction is (p − 1)− linear and resonant with respect to principal eigenvalue of ( −△p;W1,p 0 (Ω) ) : Our approach uses variational methods based on the critical point theory, together with suitable truncation and comparison techniques and Morse theory (critical groups).