{"title":"Concentration of nodal solutions for semiclassical quadratic Choquard equations","authors":"Lu Yang, Xiangqing Liu, Jianwen Zhou","doi":"10.58997/ejde.2023.75","DOIUrl":null,"url":null,"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. For more information see https://ejde.math.txstate.edu/Volumes/2023/75/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"431 ","pages":"0"},"PeriodicalIF":0.8000,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.58997/ejde.2023.75","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
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. For more information see https://ejde.math.txstate.edu/Volumes/2023/75/abstr.html
期刊介绍:
All topics on differential equations and their applications (ODEs, PDEs, integral equations, delay equations, functional differential equations, etc.) will be considered for publication in Electronic Journal of Differential Equations.