Yamabe equations on infinite graphs

被引：30

作者：

Ge, Huabin ^{[1
]}

Jiang, Wenfeng ^{[2
]}

机构：

[1] Beijing Jiaotong Univ, Dept Math, Beijing 100044, Peoples R China

[2] Sun Yet Sen Univ, Sch Math Zhuhai, Zhuhai 519082, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 460卷 / 02期

关键词：

Yamabe equation; Infinite graphs; CONFORMAL DEFORMATION; DIRICHLET; EXISTENCE;

D O I：

10.1016/j.jmaa.2017.12.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We concern in this paper the graph Yamabe equation Delta u + hu = g vertical bar u vertical bar(P-2)u, with known functions h and g on an infinite graph, the prototype of which comes from the smooth Yamabe equation on an open manifold. We prove the existence of a solution to the graph Yamabe equation under the assumption that (1) the graph Laplacian Delta is a bounded operator and (2) g is bounded and h is large at infinity. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：885 / 890

页数：6

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