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},
  journal={Advances in Mathematics},
  year={2021}
}
View PDF on arXiv
4 Citations
Highly Influential Citations
1
Background Citations
2
Methods Citations
1
Results Citations
3

4 Citations

BROUWER DEGREE FOR MEAN FIELD EQUATION ON GRAPH

. Let u be a function on a connected finite graph G = ( V,E ). We consider the mean field equation (1)

Existence of solutions in the U(1) × U(1) Abelian Chern-Simons model on finite graphs

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…

Existence and asymptotic behaviors of solutions to Chern-Simons systems and equations on finite graphs

In this paper, we consider a system of equations arising from the U(1) × U(1) Abelian Chern-Simons model

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

  • Yong LinY. Yang
  • 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…

References

SHOWING 1-10 OF 24 REFERENCES

Kazdan-Warner equation on infinite graphs

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

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

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…

Kazdan–Warner equation on graph in the negative case

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…

Mean field equation and relativistic Abelian Chern-Simons model on finite graphs

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…

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…

Existence results for mean field equations

Vortex condensation in the Chern-Simons Higgs model: An existence theorem

It is shown that there is a critical value of the Chern-Simons coupling parameter so that, below the value, there exists self-dual doubly periodic vortex solutions, and, above the value, the vortices…