耦合非线性薛定谔系统的归一化峰值解的存在性

IF 3.2 1区数学 Q1 MATHEMATICS

Advances in Nonlinear Analysis Pub Date : 2024-01-01 DOI:10.1515/anona-2023-0113

Jing Yang

{"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 In this article, we study the following nonlinear Schrödinger system \n \n \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":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":3.2000,"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 In this article, we study the following nonlinear Schrödinger system \\n \\n \\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\":51301,\"journal\":{\"name\":\"Advances in Nonlinear Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.2000,\"publicationDate\":\"2024-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Nonlinear Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/anona-2023-0113\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Nonlinear Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/anona-2023-0113","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文研究以下非线性薛定谔系统 - Δ u 1 + V 1 ( x ) u 1 = α u 1 u 2 + μ u 1 , x∈ R 4 , - Δ u 2 + V 2 ( x )

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Existence of normalized peak solutions for a coupled nonlinear Schrödinger system

In this article, we study the following nonlinear Schrödinger system − Δ u 1 + V 1 ( x ) u 1 = α u 1 u 2 + μ u 1 , x ∈ R 4 , − Δ u 2 + V 2 ( x ) u 2 = α 2 u 1 2 + β u 2 2 + μ u 2 , x ∈

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Advances in Nonlinear Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

6.00

自引率

9.50%

发文量

审稿时长

30 weeks

期刊介绍： Advances in Nonlinear Analysis (ANONA) aims to publish selected research contributions devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The Journal focuses on papers that address significant problems in pure and applied nonlinear analysis. ANONA seeks to present the most significant advances in this field to a wide readership, including researchers and graduate students in mathematics, physics, and engineering.

京公网安备 11010802042870号

Book学术文献互助群
群号：481959085