Abstract
This paper studies the existence and multiplicity of normalized solutions to the lower critical Choquard equation with a $L^2$-subcritical local perturbation and kinds of bounded potentials\begin{equation*}\begin{cases}-\Delta u+V(x)u\\\qquad =\lambda u+\big(I_{\alpha}\ast|u|^{({N+\alpha})/{N}}\big)|u|^{({N+\alpha})/{N}-2}u+\mu|u|^{q-2}u& \text{in } \mathbb{R}^N, \\\displaystyle\int_{\mathbb{R}^N}|u|^2dx=a^2,\end{cases}\end{equation*}where $N\geq 1$, $\mu, a> 0$, $2< q< 2+{4}/{N}$, $\alpha\in (0,N)$, $I_{\alpha}$ is the Riesz potential, $V(x)$ is a bounded potential and $\lambda\in \mathbb{R}$ is an unknown parameter that appears as a Lagrange multiplier.
Citation
Xinfu Li. Li Xu. "Existence and multiplicity of normalized solutions to lower critical Choquard equation with kinds of bounded potentials." Topol. Methods Nonlinear Anal. Advance Publication 1 - 26, 2024. https://doi.org/10.12775/TMNA.2023.042
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