Existence theorems for a generalized Chern-Simons equation on finite graphs

Jia Gao, Songbo Hou

Denote by $G=(V,E)$ a finite graph. We study a generalized Chern-Simons equation $$\Delta u=\lambda {\mathrm{e}}^u({\mathrm{e}}^{bu}-1)+4\pi \sum _{j=1}^N{\delta }_{p_j}$$ on $G$, where $\lambda$ and $b$…