{"title":"耦合非线性薛定谔系统的归一化峰值解的存在性","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":"{\"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 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引用次数: 0