On weak solutions to a fractional Hardy--Hénon equation: Part I: Nonexistence

Abstract

This paper and [17] treat the existence and nonexistence of stable (resp. outside stable) weak solutions to a fractional Hardy--Hénon equation $(-\Delta {)}^{s}u=|x{|}^{\ell }|u{|}^{p-1}u$ in ${\mathbb{R}}^N$ where $0<s<1$, $\ell >-2s$, $p>1$, $N\ge 1$ and $N>2s$. In this paper, the nonexistence part is proved for the Joseph--Lundgren subcritical case.