Infinitely many non-radial solutions to a critical Choquard equation
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912494934556672 |
|---|---|
| author | Caputo, Sabrina Vaira, Giusi |
| author_facet | Caputo, Sabrina Vaira, Giusi |
| contents | In this paper we study a class of critical Choquard equations with a symmetric potential, i.e. we consider the equation $$-Δu +V(|x|) u =\left(|x|^{-μ}* |u|^{2^\star_μ}\right)|u|^{2^\star_μ-2}u,\quad\mbox{in}\quad\mathbb R^N$$ where $V(|x|)$ is a bounded, nonnegative and symmetric potential in $\mathbb R^N$ with $N\geq 5$, $0<μ\leq 4$, $*$ stands for the standard convolution and $2^\star_μ:=\frac{2N-μ}{N-2}$ is the upper critical exponent in the sense of the Hardy - Littlewood - Sobolev inequality. By applying a finite dimensional reduction method we prove that if $r^2V(r)$ has a local maximum point or local minimum point $r_0>0$ with $V(r_0)>0$ then the problem has infinitely many non-radial solutions with arbitrary large energies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15747 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinitely many non-radial solutions to a critical Choquard equation Caputo, Sabrina Vaira, Giusi Analysis of PDEs In this paper we study a class of critical Choquard equations with a symmetric potential, i.e. we consider the equation $$-Δu +V(|x|) u =\left(|x|^{-μ}* |u|^{2^\star_μ}\right)|u|^{2^\star_μ-2}u,\quad\mbox{in}\quad\mathbb R^N$$ where $V(|x|)$ is a bounded, nonnegative and symmetric potential in $\mathbb R^N$ with $N\geq 5$, $0<μ\leq 4$, $*$ stands for the standard convolution and $2^\star_μ:=\frac{2N-μ}{N-2}$ is the upper critical exponent in the sense of the Hardy - Littlewood - Sobolev inequality. By applying a finite dimensional reduction method we prove that if $r^2V(r)$ has a local maximum point or local minimum point $r_0>0$ with $V(r_0)>0$ then the problem has infinitely many non-radial solutions with arbitrary large energies. |
| title | Infinitely many non-radial solutions to a critical Choquard equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.15747 |