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{"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":"2 5","pages":""},"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\":\"2 5\",\"pages\":\"\"},\"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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期刊介绍:
ACS Applied Electronic Materials is an interdisciplinary journal publishing original research covering all aspects of electronic materials. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials science, engineering, optics, physics, and chemistry into important applications of electronic materials. Sample research topics that span the journal's scope are inorganic, organic, ionic and polymeric materials with properties that include conducting, semiconducting, superconducting, insulating, dielectric, magnetic, optoelectronic, piezoelectric, ferroelectric and thermoelectric.
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