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

Antonio Iannizzotto;Vasile Staicu

2020-01-01

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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.