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arXiv · 1902.08392

Existence of Positive Solutions for a class of Quasilinear Schr\"{o}dinger Equations of Choquard type

Shaoxiong Chen·Xian Wu
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Abstract

In this paper, we study the following quasilinear Schr\"{o}dinger equation of Choquard type $$ -\triangle u+V(x)u-\triangle (u^{2})u=(I_\alpha *|u|^p)|u|^{p-2}u, \ \ x \in \mathbb{R}^{N}, $$ where $N\geq 3$,\ $0<\alpha<N$, $\frac{2(N+\alpha)}{N}\leq p<\frac{2(N+\alpha)}{N-2}$ and $I_\alpha$ is a Riesz potential. Under appropriate assumptions on $V(x)$, we establish the existence of positive solutions.

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Shaoxiong Chen, Xian Wu. 2019-02-22. Existence of Positive Solutions for a class of Quasilinear Schr\"{o}dinger Equations of Choquard type. https://arxiv.org/abs/1902.08392

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