{"title":"Ground state solutions of Schrödinger system with fractional p-Laplacian","authors":"Yanyou Qiao, Fangqi Chen, Yukun An","doi":"10.1515/ijnsns-2022-0112","DOIUrl":null,"url":null,"abstract":"Abstract This article deals with a class of nonlinear fractional p-Laplacian Schr o ̈ $\\ddot{o}$ dinger coupled system with critical and subcritical nonlinear terms. Firstly, the existence of a nonnegative ground state solution of the system is proved by the Nehari manifold method and the Ekeland’s variational principle. In addition, through the Ljusternik–Schnirelmann theory, we link the number of solutions to the topology of the set in which the potentials in the system reach their minimum values.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1515/ijnsns-2022-0112","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract This article deals with a class of nonlinear fractional p-Laplacian Schr o ̈ $\ddot{o}$ dinger coupled system with critical and subcritical nonlinear terms. Firstly, the existence of a nonnegative ground state solution of the system is proved by the Nehari manifold method and the Ekeland’s variational principle. In addition, through the Ljusternik–Schnirelmann theory, we link the number of solutions to the topology of the set in which the potentials in the system reach their minimum values.
研究一类非线性分数阶p-拉普拉斯Schr o ø $\ddot{o}$ dinger耦合系统，该系统具有临界和次临界非线性项。首先，利用Nehari流形方法和Ekeland变分原理证明了系统非负基态解的存在性。此外，通过Ljusternik-Schnirelmann理论，我们将解的个数与系统中势达到最小值的集合拓扑联系起来。
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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