# Brouwer degree for Kazdan-Warner equations on a connected finite graph

@article{Sun2021BrouwerDF,
title={Brouwer degree for Kazdan-Warner equations on a connected finite graph},
author={Linlin Sun and Liuquan Wang},
year={2021}
}
• Published 20 April 2021
• Mathematics
. Let u be a function on a connected ﬁnite graph G = ( V,E ). We consider the mean ﬁeld equation (1)
• Mathematics
• 2022
In this paper, we consider a system of equations arising from the U(1) × U(1) Abelian Chern-Simons model on ﬁnite graphs. Here λ > 0, b > a > 0, m j > 0 ( j = 1 , 2 , ··· k 1 ), n j > 0 j = 1 2 ··· k
• Mathematics
• 2022
In this paper, we consider a system of equations arising from the U(1) × U(1) Abelian Chern-Simons model
• Mathematics
Calculus of Variations and Partial Differential Equations
• 2021
Inspired by works of Castéras (Pac J Math 276:321–345, 2015), Li and Zhu (Calc Var Partial Differ Equ 58:1–18, 2019), Sun and Zhu (Calc Var Partial Differ Equ 60:1–26, 2021), we propose a heat flow

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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
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