Neumann fractional [formula omitted]-Laplacian: Eigenvalues and existence results

Abstract

We develop some properties of the p-Neumann derivative for the fractional p-Laplacian in bounded domains with general p>1. In particular, we prove the existence of a diverging sequence of eigenvalues and we introduce the evolution problem associated to such operators, studying the basic properties of solutions. Finally, we study a nonlinear problem with source in absence of the Ambrosetti–Rabinowitz condition.