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

Authors: 

Anh Tuan Duong, Vu Trong Luong, Thi Quynh Nguyen

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

a.

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

a

or equivalently

p > pc(N,s,a),

where

a