Linking over cones for the Neumann Fractional $p-$Laplacian

Abstract

We consider nonlinear problems governed by the fractional p−Laplacian in presence of nonlocal Neumann boundary conditions. We face two problems. First: the p−superlinear term may not satisfy the Ambrosetti-Rabinowitz condition. Second, and more important: although the topological structure of the underlying functional reminds the one of the linking theorem, the nonlocal nature of the associated eigenfunctions prevents the use of such a classical theorem. For these reasons, we are led to adopt another approach, relying on the notion of linking over cones.