Multiple solutions for p-Laplacian type problems with asymptotically p-linear terms via a cohomological index theory

The aim of this paper is investigating the existence of weak solutions of a quasilinear elliptic model problem of p-Laplacian type with Dirichlet boundary conditions on a bounded domain in the N-dimensional Euclidean space when the nonlinear term is asymptotically p-linear at infinity. Under suitable hypotheses both at the origin and at infinity, and in assumptions of symmetry, by using variational tools, a cohomological index theory and a related pseudo-index argument, we prove a multiplicity result if p > N in the non-resonant case.