Existence results for some nonlinear elliptic systems on graphs

IF 1.2 3区 数学 Q1 MATHEMATICS Journal of Mathematical Analysis and Applications Pub Date : 2024-10-16 DOI:10.1016/j.jmaa.2024.128973
Shoudong Man
{"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":1.2000,"publicationDate":"2024-10-16","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":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

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.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
图上某些非线性椭圆系统的存在性结果
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。
求助全文
约1分钟内获得全文 去求助
来源期刊
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.
期刊最新文献
Analysis of SIS infectious disease dynamics with linear external sources and free boundaries: A computational and theoretical perspective Boundedness and global existence in a higher-dimensional parabolic-elliptic-ODE chemotaxis-haptotaxis model with remodeling of non-diffusible attractant Asymptotic expansions for the generalised trigonometric integral and its zeros Semiclassical limit of a non-polynomial q-Askey scheme Free boundary problem governed by a non-linear diffusion-convection equation with Neumann condition
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1