Existence of normalized solutions to Choquard equation with general mixed nonlinearities
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917752145444864 |
|---|---|
| author | Zhu, Meiling Li, Xinfu |
| author_facet | Zhu, Meiling Li, Xinfu |
| contents | We study the existence of normalized solutions to the following Choquard equation with $F$ being a Berestycki-Lions type function \begin{equation*} \begin{cases} -Δu+λu=(I_α\ast F(u))f(u),\quad \text{in}\ \mathbb{R}^N, \\ \int_{\mathbb{R}^N}|u|^2dx=ρ^2, \end{cases} \end{equation*} where $N\geq 3$, $ρ>0$ is assigned, $α\in (0,N)$, $I_α$ is the Riesz potential, and $λ\in \mathbb{R}$ is an unknown parameter that appears as a Lagrange multiplier. Here, the general nonlinearity $F$ contains the $L^2$-subcritical and $L^2$-supercritical mixed case, the Hardy-Littlewood-Sobolev lower critical and upper critical cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09900 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of normalized solutions to Choquard equation with general mixed nonlinearities Zhu, Meiling Li, Xinfu Analysis of PDEs We study the existence of normalized solutions to the following Choquard equation with $F$ being a Berestycki-Lions type function \begin{equation*} \begin{cases} -Δu+λu=(I_α\ast F(u))f(u),\quad \text{in}\ \mathbb{R}^N, \\ \int_{\mathbb{R}^N}|u|^2dx=ρ^2, \end{cases} \end{equation*} where $N\geq 3$, $ρ>0$ is assigned, $α\in (0,N)$, $I_α$ is the Riesz potential, and $λ\in \mathbb{R}$ is an unknown parameter that appears as a Lagrange multiplier. Here, the general nonlinearity $F$ contains the $L^2$-subcritical and $L^2$-supercritical mixed case, the Hardy-Littlewood-Sobolev lower critical and upper critical cases. |
| title | Existence of normalized solutions to Choquard equation with general mixed nonlinearities |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.09900 |