A weighted (p,2)-equation with double resonance

Abstract

We consider a Dirichlet problem driven by a weighted (p,2)-Laplacian with a reaction which is resonant both at \(\pm\infty\) and at zero (double resonance). We prove a multiplicity theorem producing three nontrivial smooth solutions with sign information and ordered. In the appendix we develop the spectral properties of the weighted r-Laplace differential operator.