Existence of periodic solutions for 2$n$th-order nonlinear $p$-Laplacian difference equations

Abstract

By using the critical point theory, the existence of periodic solutions for 2nth-order nonlinear p-Laplacian difference equations 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 2nth-order p-Laplacian difference equations. The results obtained successfully generalize and complement the existing ones. 2010 AMS Mathematics subject classification. Primary 39A11.

On variational and topological methods in nonlinear difference equations

“…Since 2003, the critical point theory has been extensively applied to study the existence and multiplicity of periodic solutions and boundary value problems to difference equations involving a p-Laplacian operator (more generally, ϕ-Laplacian operator) and higher order difference equations (cf. [3,20,21,22,27,32,51,67,72,84,114]. In this section, we only list several results in the literature.…”

“…In recent years, Shi and his collaborators have contributed a lot on higher order difference equations (we refer to [84,86] and references therein for details).…”