Existence of Periodic Solutions for a 2 $$n$$ n th-Order Difference Equation Involving $$p$$ p -Laplacian

Abstract

Using the critical point theory, the existence of periodic solutions for a 2\(n\)th-order nonlinear difference equation containing both advance and retardation involving \(p\)-Laplacian is obtained. The main approaches used in our paper are variational techniques and the Saddle Point Theorem. The problem is to solve the existence of periodic solutions for a 2\(n\)th-order \(p\)-Laplacian difference equation. The obtained results successfully generalize and complement the existing ones.