Kazdan-Warner equation on infinite graphs

Abstract

We concern in this paper the graph Kazdan-Warner equation \begin{equation*} Δf=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 $h\le 0$ and some other integrability conditions or constrictions about the underlying infinite graphs.

References in corpus (2)

• Kazdan-Warner equation on graph in the negative case
• p-th Kazdan-Warner equation on graph

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