The 1-Yamabe equation on graphs

被引：15
|
作者：
Ge, Huabin [1 ]
Jiang, Wenfeng [2 ]
机构：
[1] Renmin Univ China, Sch Math, Beijing 100872, Peoples R China
[2] Sun Yet Sen Univ, Sch Math Zhuhai, Zhuhai 519082, Peoples R China
来源：
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2019年 / 21卷 / 08期
关键词：
1-Laplacian; Yamabe equation; graphs; KAZDAN-WARNER EQUATION; CONFORMAL DEFORMATION; 1-LAPLACIAN; EXISTENCE; CONSTANT; SPECTRUM;
D O I：
10.1142/S0219199718500402
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the following 1-Yamabe equation on connected finite graphs Delta(1)u + gSgn (u) = h vertical bar u vertical bar(alpha-1) Sgn (u), where Delta(1) is the discrete 1-Laplacian, alpha > 1 and g, h > 0 are known. We show that the above 1-Yamabe equation always has a nontrivial solution u >= 0, u not equal 0.
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页数：10
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