图的随机完备性的非线性表征

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2025-02-12 DOI:10.1002/mana.202400436

Marcel Schmidt, Ian Zimmermann

{"title":"图的随机完备性的非线性表征","authors":"Marcel Schmidt, Ian Zimmermann","doi":"10.1002/mana.202400436","DOIUrl":null,"url":null,"abstract":"<p>We study nonlinear Schrödinger operators on graphs. We construct minimal nonnegative solutions to corresponding semilinear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a nonlinear setting. We provide characterizations for this property in terms of a semilinear Liouville theorem. It is employed to establish a nonlinear characterization for stochastic completeness, which is a graph version of a recent result on Riemannian manifolds.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"925-943"},"PeriodicalIF":0.8000,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400436","citationCount":"0","resultStr":"{\"title\":\"A nonlinear characterization of stochastic completeness of graphs\",\"authors\":\"Marcel Schmidt, Ian Zimmermann\",\"doi\":\"10.1002/mana.202400436\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study nonlinear Schrödinger operators on graphs. We construct minimal nonnegative solutions to corresponding semilinear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a nonlinear setting. We provide characterizations for this property in terms of a semilinear Liouville theorem. It is employed to establish a nonlinear characterization for stochastic completeness, which is a graph version of a recent result on Riemannian manifolds.</p>\",\"PeriodicalId\":49853,\"journal\":{\"name\":\"Mathematische Nachrichten\",\"volume\":\"298 3\",\"pages\":\"925-943\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-02-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400436\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematische Nachrichten\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mana.202400436\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Nachrichten","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.202400436","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们研究图上的非线性Schrödinger算子。构造了相应的半线性椭圆方程的极小非负解，并利用它们引入了非线性无穷远处随机完备性的概念。我们用半线性刘维尔定理来描述这个性质。它被用来建立随机完备性的非线性表征，这是最近关于黎曼流形的一个结果的图版本。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A nonlinear characterization of stochastic completeness of graphs

We study nonlinear Schrödinger operators on graphs. We construct minimal nonnegative solutions to corresponding semilinear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a nonlinear setting. We provide characterizations for this property in terms of a semilinear Liouville theorem. It is employed to establish a nonlinear characterization for stochastic completeness, which is a graph version of a recent result on Riemannian manifolds.

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

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index