Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.00708 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- In this paper, we consider the radial symmetry, uniqueness and non-degeneracy of solutions to the degenerate nonlinear elliptic equation $$ -\nabla \cdot \left(|x|^{2a} \nabla u\right) + ωu=|u|^{p-2}u \quad \mbox{in} \,\, \R^d, $$ where $d \geq 2$, $0<a<1$, $ω>0$ and $2<p<\frac{2d}{d-2(1-a)}$. We proved that any ground state is radially symmetric and strictly decreasing in the radial direction. Moreover, we establish the uniqueness of ground states and derive the non-degeneracy of ground states in the corresponding radially symmetric Sobolev space. This affirms the natural conjectures posed recently in \cite{IS}.