Existence and multiplicity results for partial differential inclusions via nonsmooth local linking

Abstract

We consider a partial differential inclusion driven by the p-Laplacian and involving a nonsmooth potential, with Dirichlet boundary conditions. Under convenient assumptions on the behavior of the potential near the origin, the associated energy functional has a local linking. By means of nonsmooth Morse theory, we prove the existence of at least one or two nontrivial solutions, respectively, when the potential is p-superlinear or at most asymptotically p-linear at infinity.