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 RN, 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.
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - 2023 Feb|
- Fractional Hardy–Hénon equation
- Separation property
- Stable solutions
ASJC Scopus subject areas
- Applied Mathematics