图上某些非线性椭圆系统的存在性结果

IF 1.3 3区数学 Q1 MATHEMATICS Journal of Mathematical Analysis and Applications Pub Date : 2025-03-15 Epub Date: 2024-10-16 DOI:10.1016/j.jmaa.2024.128973

Shoudong Man

{"title":"图上某些非线性椭圆系统的存在性结果","authors":"Shoudong Man","doi":"10.1016/j.jmaa.2024.128973","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, several nonlinear elliptic systems are investigated on graphs. One type of the Sobolev embedding theorem and a new version of the strong maximum principle are established. Then, by using the variational method, the existence of different types of solutions to some elliptic systems is confirmed. Such problems extend the existence results on closed Riemann surface to graphs and extend the existence results for one single equation on graphs by Grigor'yan et al. (2016) <span><span>[12]</span></span> to nonlinear elliptic systems on graphs. Such problems can also be viewed as one type of discrete version of the elliptic systems on Euclidean space and Riemannian manifold.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128973"},"PeriodicalIF":1.3000,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence results for some nonlinear elliptic systems on graphs\",\"authors\":\"Shoudong Man\",\"doi\":\"10.1016/j.jmaa.2024.128973\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, several nonlinear elliptic systems are investigated on graphs. One type of the Sobolev embedding theorem and a new version of the strong maximum principle are established. Then, by using the variational method, the existence of different types of solutions to some elliptic systems is confirmed. Such problems extend the existence results on closed Riemann surface to graphs and extend the existence results for one single equation on graphs by Grigor'yan et al. (2016) <span><span>[12]</span></span> to nonlinear elliptic systems on graphs. Such problems can also be viewed as one type of discrete version of the elliptic systems on Euclidean space and Riemannian manifold.</div></div>\",\"PeriodicalId\":50147,\"journal\":{\"name\":\"Journal of Mathematical Analysis and Applications\",\"volume\":\"543 2\",\"pages\":\"Article 128973\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2025-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022247X24008953\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2024/10/16 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24008953","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/10/16 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了图上的几个非线性椭圆系统。建立了一种 Sobolev 嵌入定理和新版强最大原则。然后，通过使用变分法，证实了一些椭圆系统不同类型解的存在性。这类问题将封闭黎曼曲面上的存在性结果扩展到了图上，并将格里高利等人（2016）[12] 对图上一个单方程的存在性结果扩展到了图上的非线性椭圆系统。这类问题也可视为欧几里得空间和黎曼流形上椭圆系统的一种离散版本。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Existence results for some nonlinear elliptic systems on graphs

In this paper, several nonlinear elliptic systems are investigated on graphs. One type of the Sobolev embedding theorem and a new version of the strong maximum principle are established. Then, by using the variational method, the existence of different types of solutions to some elliptic systems is confirmed. Such problems extend the existence results on closed Riemann surface to graphs and extend the existence results for one single equation on graphs by Grigor'yan et al. (2016) [12] to nonlinear elliptic systems on graphs. Such problems can also be viewed as one type of discrete version of the elliptic systems on Euclidean space and Riemannian manifold.

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

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.