On weak solutions to a fractional Hardy–Hénon equation, Part II: Existence

This paper and Hasegawa et al. (2021) treat the existence and nonexistence of stable weak solutions to a fractional Hardy–Hénon equation (−Δ)^su=|x|^ℓ|u|^p−1u 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∈(0,∞) and s∈(0,1), and this property does not hold in the case s=1.