Multiple periodic solutions for two classes of nonlinear difference systems involving classical $(\phi_1,\phi_2)$-Laplacian

TL;DR

This paper proves the existence of multiple periodic solutions for two classes of nonlinear difference systems involving the $(eta_1,eta_2)$-Laplacian, using critical point theorems and providing concrete examples.

Contribution

It introduces new multiplicity results for nonlinear difference systems with $(eta_1,eta_2)$-Laplacian, applying advanced critical point theorems to establish multiple solutions.

Findings

Existence of three periodic solutions for the first system.

Multiple solutions for the second system under symmetry conditions.

Verification of theorems through concrete examples.

Abstract

In this paper, we investigate the existence of multiple periodic solutions for two classes of nonlinear difference systems involving $(\phi_1,\phi_2)$-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 $(\phi_1,\phi_2)$-Laplacian and two parameters. Moreover, for the second nonlinear difference system with $(\phi_1,\phi_2)$-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.