Classification of Stable Solutions to a Fractional Singular Elliptic Equation with Weight
Classification of Stable Solutions to a Fractional Singular Elliptic Equation with Weight
Source title:
Acta Applicandae Mathematicae, 170: 579-591,
2020
(ISI)
Academic year of acceptance:
2020-2021
Abstract:
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 > pc(N,s,a),
where