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

Shoichi Hasegawa, Norihisa Ikoma, Tatsuki Kawakami

Research output: Contribution to journalArticlepeer-review


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||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.

Original languageEnglish
Article number113165
JournalNonlinear Analysis, Theory, Methods and Applications
Publication statusPublished - 2023 Feb


  • Fractional Hardy–Hénon equation
  • Separation property
  • Stable solutions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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