Existence of Solutions to a Class of Kazdan-Warner Equations on Finite Graphs

Yi Li, Qianwei Zhang

Let $G=(V,E)$ be a connected finite graph, $h$ be a positive function on $V$ and ${\lambda }_1(V)$ be the first non-zero eigenvalue of $-\Delta$. For any given finite measure $\mu$ on $V$, defi…