The Hénon equation beyond the critical Sobolev exponent
We consider the Dirichlet problem $-Δu=|x|^αu^p$, $u>0$ in $Ω$, $u=0$ on $\partialΩ$, where $Ω\subset R^N$, $N\ge 3$, is a bounded domain containing the origin and $α>0$. We prove that a solution exists for every exponent $1
Authors
- Massimo Grossi (ORCID: https://orcid.org/0000-0002-1998-9336)
- Francesca Gladiali (ORCID: https://orcid.org/0000-0003-0382-8658)
Publication Details
- Journal
- arXiv (Cornell University)
- Published
- 2026-10-29
- DOI
- https://doi.org/10.48550/arxiv.2610.39976
- Primary Topic
- Nonlinear Partial Differential Equations
- Type
- preprint