Fractional elliptic problem in exterior domains with nonlocal Neumann condition

Abstract

In this paper we consider the existence of solution for the following class of fractional elliptic problem (0.1)(−Δ)su+u=Q(x)|u|p−1uinRN∖ΩNsu(x)=0inΩ,where s∈(0,1), N>2s, Ω⊂RN is a bounded set with smooth boundary, (−Δ)s denotes the fractional Laplacian operator and Ns is the nonlocal operator that describes the Neumann boundary condition, which is given by Nsu(x)=CN,s∫RN∖Ωu(x)−u(y)|x−y|N+2sdy,x∈Ω.