J. Korean Math. Soc. 2018; 55(5): 1091-1101
Online first article August 6, 2018 Printed September 1, 2018
https://doi.org/10.4134/JKMS.j170561
Copyright © The Korean Mathematical Society.
Huabin Ge, Wenfeng Jiang
Beijing Jiaotong University, Sun Yat-Sen University
We concern in this paper the graph Kazdan-Warner equation \begin{equation*} \Delta f=g-he^f \end{equation*} on an infinite graph, the prototype of which comes from the smooth Kazdan-Warner equation on an open manifold. Different from the variational methods often used in the finite graph case, we use a heat flow method to study the graph Kazdan-Warner equation. We prove the existence of a solution to the graph Kazdan-Warner equation under the assumption that $h\leq0$ and some other integrability conditions or constrictions about the underlying infinite graphs.
Keywords: Kazdan-Warner equation, heat flow, infinite graph
MSC numbers: Primary 35R02; Secondary 35K55
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