{"title":"Multiple standing waves of matrix nonlinear Schrödinger equations with mixed growth nonlinearities in RN","authors":"Ting Zhang, Guanwei Chen","doi":"10.1016/j.nonrwa.2024.104153","DOIUrl":null,"url":null,"abstract":"<div><p>In the whole space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>, we study the existence of two standing waves for a class of matrix nonlinear Schrödinger equations with potentials by using variational methods, where the nonlinearities are sublinear or asymptotically linear at infinity. The novelties are as follows. (1) The matrix nonlinear equations are defined in the whole space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>. (2) The nonlinearities are composed of two mixed nonlinear terms with different growth conditions. (3) The weight function may be sign-changing. (4) Our results can be applied to many examples.</p></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121824000932","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
In the whole space , we study the existence of two standing waves for a class of matrix nonlinear Schrödinger equations with potentials by using variational methods, where the nonlinearities are sublinear or asymptotically linear at infinity. The novelties are as follows. (1) The matrix nonlinear equations are defined in the whole space . (2) The nonlinearities are composed of two mixed nonlinear terms with different growth conditions. (3) The weight function may be sign-changing. (4) Our results can be applied to many examples.
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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