Existence of Periodic Solutions for a Class of Asymptotically p -Linear Discrete Systems Involving p -Laplacian

Abstract

By applying Mountain Pass Theorem in critical point theory, two existence results are obtained for the following asymptotically $p$-linear $p$-Laplacian discrete system $\Delta \left({\left|\Delta u\left(t-1\right)\right|}^{p-2}\Delta u\left(t-1\right)\right)+\nabla \left[-K\left(t,u\left(t\right)\right)+W\left(t,u\left(t\right)\right)\right]=0$. The results obtained generalize some known works.