p-th Kazdan-Warner equation on graph in the negative case

Let G=(V,E) be a connected finite graph. Consider the p-th Kazdan-Warner equation on GΔpu=c−heu, where Δp is the discrete p-Laplacian on G with p>1, h is a known function defined on V. When c<0 and h‾<0, Ge [8] showed that there exists a negative number c−(h) such that the p-th Kazdan-Warner equation on G is solvable for every 0>c>c−(h) and is not solvable for c