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
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
相关论文
共 13 条
[1]  
[Anonymous], 1968, Ann. Scuola Norm. Sup. Pisa (3)
[2]  
Aubin T., 1976, Differential Geometry and Relativity, P5
[3]  
Ge H., 2016, ARXIV161104906
[4]   Existence of positive solutions to some nonlinear equations on locally finite graphs [J].
Grigor'yan, Alexander ;
Lin Yong ;
Yang YunYan .
SCIENCE CHINA-MATHEMATICS, 2017, 60 (07) :1311-1324
[5]   Yamabe type equations on graphs [J].
Grigor'yan, Alexander ;
Lin, Yong ;
Yang, Yunyan .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 261 (09) :4924-4943
[6]   Laplacians on infinite graphs: Dirichlet and Neumann boundary conditions [J].
Haeseler, Sebastian ;
Keller, Matthias ;
Lenz, Daniel ;
Wojciechowski, Radoslaw .
JOURNAL OF SPECTRAL THEORY, 2012, 2 (04) :397-432
[7]   EXISTENCE AND CONFORMAL DEFORMATION OF METRICS WITH PRESCRIBED GAUSSIAN AND SCALAR CURVATURES [J].
KAZDAN, JL ;
WARNER, FW .
ANNALS OF MATHEMATICS, 1975, 101 (02) :317-331
[8]   CURVATURE FUNCTIONS FOR OPEN 2-MANIFOLDS [J].
KAZDAN, JL ;
WARNER, FW .
ANNALS OF MATHEMATICS, 1974, 99 (02) :203-219
[9]  
KAZDAN JL, 1975, J DIFFERENTIAL GEOME, V10, P113
[10]   Dirichlet forms and stochastic completeness of graphs and subgraphs [J].
Keller, Matthias ;
Lenz, Daniel .
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2012, 666 :189-223