Linking over cones for the Neumann fractional p-Laplacian

We consider nonlinear problems governed by the fractional p-Laplacian in presence of nonlocal Neumann boundary conditions and we show three different existence results: first two theorems deal with a p-superlinear term, last one source having p-linear growth. For case face main difficulties. First: term may not satisfy Ambrosetti-Rabinowitz condition. Second, more important: although topological structure underlying functional reminds linking theorem, nature associated eigenfunctions prevents use such classical theorem. these reasons, are led to adopt another approach, relying on notion over cones.