On a resonance problem with the discrete p-Laplacian on finite graphs

Abstract

In this paper, we discuss the existence of a solution for a resonance problem involving the discrete p-Laplacian. Using asymptotic behaviors of g at infinity, a nontrivial solution is established. Moreover, we also find a necessary condition for asymptotic behavior of g at zero to guarantee the existence of at least two nontrivial solutions. © 2011 Elsevier Ltd. All rights reserved.