Existence and multiplicity of normalized solutions to lower critical Choquard equation with kinds of bounded potentials
DOI:
https://doi.org/10.12775/TMNA.2023.042Keywords
Normalized solutions, existence, multiplicity, lower critical Choquard equation, bounded potentialsAbstract
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.References
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