Multiple periodic solutions for two classes of nonlinear difference systems involving classical $({\varphi }_1,{\varphi }_2)$-Laplacian

Abstract

In this paper, we investigate the existence of multiple periodic solutions for two classes of nonlinear difference systems involving $({\varphi }_1,{\varphi }_2)$-Laplacian. First, by using an important critical point theorem due to B. Ricceri, we establish an existence theorem of three periodic solutions for the first nonlinear difference system with $({\varphi }_1,{\varphi }_2)$-Laplacian and two parameters. Moreover, for the second nonlinear difference system with $({\varphi }_1,{\varphi }_2)$-Laplacian, by using the Clark's Theorem, we obtain a multiplicity result of periodic solutions under a symmetric condition. Finally, two examples are given to verify our theorems.