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 - Δ p u + h (x) | u | p - 2 u = f (x , u) + g (x) on the locally finite graph G, where Δ 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. [ABSTRACT FROM AUTHOR]