Classification of Stable Solutions to a Fractional Singular Elliptic Equation with Weight

Let p > 0 and (−Δ)^s is the fractional Laplacian with 0 < s < 1. The purpose of this paper is to establish a classification result for positive stable solutions to a fractional singular elliptic equation with weight

.

Here N > 2s and h is a nonnegative, continuous function satisfying h(x) ≥ C|x|^a, a ≥ 0, when |x| large. We prove the nonexistence of positive stable solutions of this equation under the condition

or equivalently

p > p_c(N,s,a),

where