ELLIPTIC PROBLEM IN AN EXTERIOR DOMAIN DRIVEN BY A SINGULARITY WITH A NONLOCAL NEUMANN CONDITION

Abstract

We prove existence of a ground state solution to the following problem. (Formula presented) where N \geq 2, \lambda > 0, 0 < s, \gamma < 1, p \in (1, 2\asts -1) with (Formula presented). Moreover, (Formula presented) is a smooth bounded domain, (-\Delta)s denotes the s-fractional Laplacian and finally Ns denotes a nonlocal operator that describes the Neumann boundary condition. We further establish existence of infinitely many bounded solutions to the problem. � (2023), (Institute of Mathematics). All rights reserved.