{"title":"Existence of normalized peak solutions for a coupled nonlinear Schrödinger system","authors":"Jing Yang","doi":"10.1515/anona-2023-0113","DOIUrl":null,"url":null,"abstract":"\n <jats:p>In this article, we study the following nonlinear Schrödinger system <jats:disp-formula id=\"j_anona-2023-0113_eq_001\">\n <jats:alternatives>\n <jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anona-2023-0113_eq_001.png\" />\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\">\n <m:mfenced open=\"{\" close=\"\">\n <m:mrow>\n <m:mtable displaystyle=\"true\">\n <m:mtr>\n <m:mtd columnalign=\"left\">\n <m:mo>−</m:mo>\n <m:mi mathvariant=\"normal\">Δ</m:mi>\n <m:msub>\n <m:mrow>\n <m:mi>u</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>1</m:mn>\n </m:mrow>\n </m:msub>\n <m:mo>+</m:mo>\n <m:msub>\n <m:mrow>\n <m:mi>V</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>1</m:mn>\n </m:mrow>\n </m:msub>\n <m:mrow>\n <m:mo>(</m:mo>\n <m:mrow>\n <m:mi>x</m:mi>\n </m:mrow>\n <m:mo>)</m:mo>\n </m:mrow>\n <m:msub>\n <m:mrow>\n <m:mi>u</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>1</m:mn>\n </m:mrow>\n </m:msub>\n <m:mo>=</m:mo>\n <m:mi>α</m:mi>\n <m:msub>\n <m:mrow>\n <m:mi>u</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>1</m:mn>\n </m:mrow>\n </m:msub>\n <m:msub>\n <m:mrow>\n <m:mi>u</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>2</m:mn>\n </m:mrow>\n </m:msub>\n <m:mo>+</m:mo>\n <m:mi>μ</m:mi>\n <m:msub>\n <m:mrow>\n <m:mi>u</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>1</m:mn>\n </m:mrow>\n </m:msub>\n <m:mo>,</m:mo>\n </m:mtd>\n <m:mtd columnalign=\"left\">\n <m:mi>x</m:mi>\n <m:mo>∈</m:mo>\n <m:msup>\n <m:mrow>\n <m:mi mathvariant=\"double-struck\">R</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>4</m:mn>\n </m:mrow>\n </m:msup>\n <m:mo>,</m:mo>\n </m:mtd>\n </m:mtr>\n <m:mtr>\n <m:mtd columnalign=\"left\">\n <m:mo>−</m:mo>\n <m:mi mathvariant=\"normal\">Δ</m:mi>\n <m:msub>\n <m:mrow>\n <m:mi>u</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>2</m:mn>\n </m:mrow>\n </m:msub>\n <m:mo>+</m:mo>\n <m:msub>\n <m:mrow>\n <m:mi>V</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>2</m:mn>\n </m:mrow>\n </m:msub>\n <m:mrow>\n <m:mo>(</m:mo>\n <m:mrow>\n <m:mi>x</m:mi>\n </m:mrow>\n <m:mo>)</m:mo>\n </m:mrow>\n <m:msub>\n <m:mrow>\n <m:mi>u</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>2</m:mn>\n </m:mrow>\n </m:msub>\n <m:mo>=</m:mo>\n <m:mfrac>\n <m:mrow>\n <m:mi>α</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>2</m:mn>\n </m:mrow>\n </m:mfrac>\n <m:msubsup>\n <m:mrow>\n <m:mi>u</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>1</m:mn>\n </m:mrow>\n <m:mrow>\n <m:mn>2</m:mn>\n </m:mrow>\n </m:msubsup>\n <m:mo>+</m:mo>\n <m:mi>β</m:mi>\n <m:msubsup>\n <m:mrow>\n <m:mi>u</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>2</m:mn>\n </m:mrow>\n <m:mrow>\n <m:mn>2</m:mn>\n </m:mrow>\n </m:msubsup>\n <m:mo>+</m:mo>\n <m:mi>μ</m:mi>\n <m:msub>\n <m:mrow>\n <m:mi>u</m:mi>\n </m:mrow>\n <m:mrow>\n <m:mn>2</m:mn>\n </m:mrow>\n </m:msub>\n <m:mo>,</m:mo>\n </m:mtd>\n <m:mtd columnalign=\"left\">\n <m:mi>x</m:mi>\n <m:mo>∈</m:mo>\n <m:msup>\n <m:mrow>\n <m:m","PeriodicalId":3,"journal":{"name":"ACS Applied Electronic Materials","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Electronic Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/anona-2023-0113","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0