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}
}

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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

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