The influence of a Generalized Hardy-Type Potential on Finite Morse Index Solutions of the Hénon Problem: Local and Nonlocal Cases
Year: 2026
Type: preprint
Abstract: In this paper, we investigate nonexistence results for stable solutions of the semilinear elliptic problem $$(-Δ)^s u+λ|x|^αu=|x|^β|u|^{p-1}u \; \mbox{in}\; \mathcal{H}, $$ where $\mathcal{H}=\mathbb{R}^n$ or $\mathcal{H}=\mathbb{R}^n_+=\{x=(x',x_n),\, x'\in\mathbb{R}^{n-1},x_n>0\}$ , with Dirichlet conditions in the half-space case. We assume that $n\geq2s$, $p>1$, $λ>0,$ $α, β>-2s$ and $0
Source: arXiv (Cornell University)
Authors: Fourti, Habib, Selmi, Abdelbaki, Zaidi, Cherif
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220715388