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

@article{Sun2022BrouwerDF,
title={Brouwer degree for Kazdan-Warner equations on a connected finite graph},
author={Linlin Sun and Liuquan Wang},
year={2022}
}
• Published 20 April 2021
• Mathematics
2 Citations

A heat flow for the mean field equation on a finite graph

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Calculus of Variations and Partial Differential Equations
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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

Existence of solutions in the $\text{U}(1)\times \text{U}(1)$ Abelian Chern-Simons model on finite graphs

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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

References

SHOWING 1-10 OF 24 REFERENCES

Kazdan-Warner equation on infinite graphs

• Mathematics
• 2017
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

The Kazdan–Warner equation on canonically compactifiable graphs

• Mathematics
• 2017
We study the Kazdan–Warner equation on canonically compactifiable graphs. These graphs are distinguished as analytic properties of Laplacians on these graphs carry a strong resemblance to Laplacians

Kazdan–Warner equation on graph

• Mathematics
• 2016
Let $$G=(V,E)$$G=(V,E) be a connected finite graph and $$\Delta$$Δ be the usual graph Laplacian. Using the calculus of variations and a method of upper and lower solutions, we give various

Harnack Type Inequality: the Method of Moving Planes

Abstract:A Harnack type inequality is established for solutions to some semilinear elliptic equations in dimension two. The result is motivated by our approach to the study of some semilinear

EXISTENCE RESULT FOR THE MEAN FIELD PROBLEM ON RIEMANN SURFACES OF ALL GENUSES

Given a compact surface (Σ,g), we prove the existence of a solution for the mean field equation on Σ. The problem consists of solving a second-order nonlinear elliptic equation with variational

Multiple solutions of Kazdan–Warner equation on graphs in the negative case

• Mathematics
Calculus of Variations and Partial Differential Equations
• 2020
Let G=(V,E)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}

Nontopological N‐vortex condensates for the self‐dual Chern‐Simons theory

We prove the existence of nontopological N‐vortex solutions for an arbitrary number N of vortex points for the self‐dual Chern‐Simons‐Higgs theory with 't Hooft “periodic” boundary conditions. We use