Multiplicity results for nonlocal critical problems involving Hardy potential in the whole space

Abstract

The aim of this paper is to study a nonlocal elliptic problem in (denoted as below) involving the fractional Laplacian, a linear Hardy potential term and a critical nonlinear term. According to suitable assumptions on the set of extremal points of the functional coefficients, we prove that has multiple positive solutions, and we determine their precise behavior near the extremal points. This work extends a previous article by the first author et al. on the local case.