The 1-Yamabe equation on graphs

被引：16

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.

引用

页数：10

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