Year: 2016
Type: preprint
Abstract: Let $G=(V,E)$ be a finite graph and $Δ$ be the usual graph Laplacian. Using the calculus of variations and a method of upper and lower solutions, we give various conditions such that the Kazdan-Warner equation $Δu=c-he^u$ has a solution on $V$, where $c$ is a constant, and $h:V\rightarrow\mathbb{R}$ is a function. We also consider similar equations involving higher order derivatives on graph. Our results can be compared with the original manifold case of Kazdan-Warner (Ann. Math., 1974).
Source: arXiv (Cornell University)
Authors: Grigor'yan, Alexander, Lin, Yong, Yang, Yunyan
Institutions: Bielefeld University, Renmin University of China
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1183854763, G6220329177, G981861455
OpenAlex ID: W2950164904