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 and we show three different existence results: the first two theorems deal with a p-superlinear term, the last one with a source having p-linear growth. For the p-superlinear case we face two main difficulties. 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.