Chern-Simons-Schrödinger系统基态归一化解的存在性

IF 1.2 4区数学 Q1 MATHEMATICS

Acta Mathematica Scientia Pub Date : 2023-11-06 DOI:10.1007/s10473-023-0620-7

Yu Mao, Xingping Wu, Chunlei Tang

{"title":"Chern-Simons-Schrödinger系统基态归一化解的存在性","authors":"Yu Mao, Xingping Wu, Chunlei Tang","doi":"10.1007/s10473-023-0620-7","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we study normalized solutions of the Chern-Simons-Schrödinger system with general nonlinearity and a potential in <i>H</i><sup>1</sup>(ℝ)<sup>2</sup>. When the nonlinearity satisfies some general 3-superlinear conditions, we obtain the existence of ground state normalized solutions by using the minimax procedure proposed by Jeanjean in [L. Jeanjean, Existence of solutions with prescribed norm for semilinear elliptic equations, Nonlinear Anal. (1997)].</p></div>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"43 6","pages":"2649 - 2661"},"PeriodicalIF":1.2000,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The existence of ground state normalized solutions for Chern-Simons-Schrödinger systems\",\"authors\":\"Yu Mao, Xingping Wu, Chunlei Tang\",\"doi\":\"10.1007/s10473-023-0620-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we study normalized solutions of the Chern-Simons-Schrödinger system with general nonlinearity and a potential in <i>H</i><sup>1</sup>(ℝ)<sup>2</sup>. When the nonlinearity satisfies some general 3-superlinear conditions, we obtain the existence of ground state normalized solutions by using the minimax procedure proposed by Jeanjean in [L. Jeanjean, Existence of solutions with prescribed norm for semilinear elliptic equations, Nonlinear Anal. (1997)].</p></div>\",\"PeriodicalId\":50998,\"journal\":{\"name\":\"Acta Mathematica Scientia\",\"volume\":\"43 6\",\"pages\":\"2649 - 2661\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-11-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Scientia\",\"FirstCategoryId\":\"1089\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10473-023-0620-7\",\"RegionNum\":4,\"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":"Acta Mathematica Scientia","FirstCategoryId":"1089","ListUrlMain":"https://link.springer.com/article/10.1007/s10473-023-0620-7","RegionNum":4,"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

在本文中，我们研究了Chern-Simons-Schrödinger系统的归一化解，该系统具有一般非线性和H1中的势(ℝ)2.当非线性满足某些一般的3-超线性条件时，我们利用Jeanjean在[L.Jeanjean，具规定范数的解的存在性，非线性分析（1997）]中提出的极大极小程序，得到了基态归一化解的存在。

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

The existence of ground state normalized solutions for Chern-Simons-Schrödinger systems

In this paper, we study normalized solutions of the Chern-Simons-Schrödinger system with general nonlinearity and a potential in H¹(ℝ)². When the nonlinearity satisfies some general 3-superlinear conditions, we obtain the existence of ground state normalized solutions by using the minimax procedure proposed by Jeanjean in [L. Jeanjean, Existence of solutions with prescribed norm for semilinear elliptic equations, Nonlinear Anal. (1997)].

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

Acta Mathematica Scientia 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

2614

审稿时长

6 months

期刊介绍： Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981. The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.