Multiple periodic solutions for two classes of nonlinear difference systems involving classical (ϕ₁,ϕ₂)-Laplacian

2016/01/02 by Xingyong Zhang, Zhang, Xingyong, Liben Wang +1
Mathematics · #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.DS

paper · pdf · doi:10.48550/arxiv.1601.00131

arxiv created 2016/01/02 · openalex publication_date 2016/01/02 · arxiv updated 2016/01/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the existence of multiple periodic solutions for two classes of nonlinear difference systems involving (ϕ₁,ϕ₂)-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 (ϕ₁,ϕ₂)-Laplacian and two parameters. Moreover, for the second nonlinear difference system with (ϕ₁,ϕ₂)-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.

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