Multiple solutions with sign information for (p, 2)−equations with asymmetric resonant reaction

Abstract

We consider a nonlinear nonhomogeneous Dirichlet problem driven by the sum of a p−Laplacian and a Laplacian (a (p, 2)− equation). The reaction is the sum of two competing terms, a parametric (p − 1)−sublinear term and an asymmetric (p − 1)−linear perturbation which is resonant at −∞. Using variational methods together with truncations and comparison techniques and Morse theory (critical groups), we prove two multiplicity theorems which provide sign information for all the solutions.