Existence results for some nonlinear elliptic systems on graphs

被引：0

作者：

Man, Shoudong ^{[1
]}

机构：

[1] Tianjin Univ Finance & Econ, Coll Sci & Technol, Zhejiang Rd, Tianjin 300222, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2025年 / 543卷 / 02期

基金：

中国国家自然科学基金;

关键词：

The Sobolev embedding theorem on graphs; Nonlinear elliptic systems on graphs; Global existence result; Local existence result; SCHRODINGER-EQUATIONS; POSITIVE SOLUTIONS;

D O I：

10.1016/j.jmaa.2024.128973

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页数：33

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