Lu Yang, Xiangqing Liu, Jianwen Zhou
Abstract:
In this article concerns the semiclassical Choquard equation
\(-\varepsilon^2 \Delta u +V(x)u = \varepsilon^{-2}( \frac{1}{|\cdot|}* u^2)u\)
for \(x \in \mathbb{R}^3\) and small \(\varepsilon\).
We establish the existence of a sequence of localized nodal solutions
concentrating near a given local minimum point of the potential function \(V\),
by means of the perturbation method and the method of invariant sets of
descending flow.
Submitted May 18, 2023. Published October 30, 2023.
Math Subject Classifications: 35B05, 35B45.
Key Words: Choquard equation; sign-changing solution; perturbation method; Fredholm operator; nodal solution.
DOI: 10.58997/ejde.2023.75
Show me the PDF file (390 KB), TEX file for this article.
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Lu Yang Department of Mathematics Yunnan University Kunming, 650091, China email: 2973434415@qq.com |
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Xiangqing Liu Department of Mathematics Yunnan Normal University Kunming, 650500, China email: lxq8u8@163.com |
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Jianwen Zhou Department of Mathematics Yunnan University Kunming, 650091, China email: jwzhou@ynu.edu.cn |
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