图上某些非线性椭圆系统的存在性结果

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-16 DOI:10.1016/j.jmaa.2024.128973

Shoudong Man

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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。

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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.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.