Existence and multiplicity of solutions to p-Laplacian equations on graphs

In this paper, we investigate the existence of multiple solutions to the nonlinear p Laplacian equation -delta(p)u + h(x)|u|(p-2)u = f(x,u) +g(x)on the locally finite graph G, where delta(p) is the discrete p-Laplacian on graphs, p >= 2. Under more general conditions, we prove that the p-Laplacian equation admits at least two nontrivial different solutions by using the variational methods and the new analytical techniques. Our results extend some related works.