Positive solutions to the nonlinear Choquard equation: symmetry, uniqueness, and nondegeneracy
We study the symmetry, uniqueness, and nondegeneracy of positive solutions to the Choquard equation $-Δu+u=(I_α*u^p)u^{p-1}$ in $\mathbb{R}^N$, which have long remained open problems. For $N\geq3$, $α\in(0,N)$, and $\frac{N+α}{N}
Authors
- Jiankang Xia (ORCID: https://orcid.org/0000-0003-2253-7469)
- Chengxiang Zhang
- Xu Zhang
Publication Details
- Journal
- arXiv (Cornell University)
- Published
- 2026-11-03
- DOI
- https://doi.org/10.48550/arxiv.2611.05138
- Primary Topic
- Nonlinear Partial Differential Equations
- Type
- preprint