Yamabe equations on infinite graphs

被引：29
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
收藏
页码：885 / 890
页数：6
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