On weak solutions to a fractional Hardy-Henon equation, Part II: Existence

This paper and Hasegawa et al. (2021) treat the existence and nonexistence of stable weak solutions to a fractional Hardy-Henon equation (-Delta)(s)u = |x|(l)|u|(p-1) u in R-N, where 0 < s < 1, l > -2s, p > 1, N >= 1 and N > 2s. In this paper, when p is critical or supercritical in the sense of the Joseph-Lundgren, we prove the existence of a family of positive radial stable solutions, which satisfies the separation property. We also show the multiple existence of the Joseph-Lundgren critical exponent for some l is an element of(0, infinity) and s is an element of (0, 1), and this property does not hold in the case s = 1. (c) 2022 Elsevier Ltd. All rights reserved.