Topological degree for Chern-Simons Higgs models on finite graphs

Jiayu Li, Linlin Sun, Yunyan Yang

Let $(V,E)$ be a finite connected graph. We are concerned about the Chern-Simons Higgs model $$\Delta u=\lambda e^u(e^u-1)+f,(0.1)$$ where $\Delta$ is the graph Lapl…