Multiple solutions for a class of quasilinear Choquard equations
• Xian Wu
Xian Wu
Yunnan Normal University
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## Abstract

In this paper, we study the following quasilinear Choquard equations of the form $$\ -\Delta u+V(x)u-\Delta (|u|^{2\alpha})|u|^{2\alpha-2}u=(|x|^{-\mu}\ast G(u))g(u), \ x \ \in R^N,$$ where $1\geq\alpha>\frac{1}{2}$, $V \in C(\mathbb{R}^N, \mathbb{R})$, $g \in C(\mathbb{R}^N, \ \mathbb{R})$. Distinguished from two situations $\lim\limits_{|x|\rightarrow\infty}V(x)=+\infty$ or $\lim\limits_{|x|\rightarrow\infty}V(x)<+\infty$, we research the existence of nontrivial solutions and a sequence of high energy solutions.

#### Peer review status:UNDER REVIEW

06 Jun 2020Submitted to Mathematical Methods in the Applied Sciences
12 Jun 2020Assigned to Editor
12 Jun 2020Submission Checks Completed
12 Jun 2020Reviewer(s) Assigned