## 4 Citations

### BROUWER DEGREE FOR MEAN FIELD EQUATION ON GRAPH

- Mathematics
- 2022

. 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

- 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…

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

- Mathematics
- 2022

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

- MathematicsCalculus 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

- 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

- Mathematics
- 1999

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

- Mathematics
- 2008

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

- Mathematics
- 2003

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…

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

- Physics
- 1995

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…