On weak solutions to a fractional Hardy--H\'enon 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--H\'enon equation $(-\Delta)^s u = |x|^\ell |u|^{p-1} u$ in $\mathbb{R}^N$ where $0 < s < 1$, $\ell > -2s$, $p>1$, $N \geq 1$ and $N > 2s$. In this paper, the nonexistence part is proved for the Joseph--Lundgren subcritical case.