Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2408.09900 |
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Inhaltsangabe:
- 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.