半经典二次Choquard方程节点解的集中

Pub Date : 2023-10-30 DOI:10.58997/ejde.2023.75

Lu Yang, Xiangqing Liu, Jianwen Zhou

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引用次数: 0

摘要

本文讨论了\(x \in \mathbb{R}^3\)和小\(\varepsilon\)的半经典Choquard方程\(-\varepsilon^2 \Delta u +V(x)u = \varepsilon^{-2}( \frac{1}{|\cdot|}* u^2)u\)。利用微扰法和降流不变集法，建立了集中于势函数\(V\)的一个给定局部极小点附近的一个局部节点解序列的存在性。欲了解更多信息，请参阅https://ejde.math.txstate.edu/Volumes/2023/75/abstr.html

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Concentration of nodal solutions for semiclassical quadratic Choquard equations

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. For more information see https://ejde.math.txstate.edu/Volumes/2023/75/abstr.html

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