Sign-changing multi-bump solutions for Choquard equation with deepening potential well
DOI:
https://doi.org/10.12775/TMNA.2021.041Keywords
Choquard equation, sign-changing solutions, multiple solutionsAbstract
In this paper, we are concerned with the existence of sign-changing multi-bump solutions for the following nonlinear Choquard equation \begin{equation}\label{eq0.1} -\Delta u+(\lambda V(x)+1)u=(I_{\alpha}\ast|u|^p)|u|^{p-2}u \quad \text{in } \mathbb{R}^N, \end{equation} where $I_\alpha$ is the Riesz potential, $\lambda \in \mathbb{R}^{+}$, $ (N-4)^{+}< \alpha< N$, $2\le p < ({N+\alpha})/({N-2})$, and $V(x)$ is a nonnegative continuous function with a potential well $\Omega:= \rom{int}(V^{-1}(0))$ which possesses $k$ disjoint bounded components $\Omega_1, \ldots, \Omega_k$. We prove the existence of sign-changing multi-bump solutions for \eqref{eq0.1} if $\lambda$ is large enough.References
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