The $1$-Yamabe equation on graph

Huabin Ge, Wenfeng Jiang

We study the following $1$-Yamabe equation on a connected finite graph $${\Delta }_{1}u+g\mathrm{Sgn}(u)=h|u{|}^{\alpha -1}\mathrm{Sgn}(u),$$ where ${\Delta }_1$ is the discrete $1$-Laplacian, $\alpha >1$ and $g,…