Linking over cones for the Neumann Fractional p-Laplacian

2020/02/11 by Mugnai, Dimitri, Lippi, Edoardo Proietti · 1 citation
#35A15 #35S15 #45G05 #47G10 #47J30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.04273

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.

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