Multiple periodic solutions for two classes of nonlinear difference systems involving classical $(ϕ_1,ϕ_2)$-Laplacian

Xingyong Zhang; Liben Wang

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arXiv · 1601.00131

Multiple periodic solutions for two classes of nonlinear difference systems involving classical $(ϕ_1,ϕ_2)$-Laplacian

Xingyong Zhang·Liben Wang

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Abstract

In this paper, we investigate the existence of multiple periodic solutions for two classes of nonlinear difference systems involving $(ϕ_1,ϕ_2)$-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 $(ϕ_1,ϕ_2)$-Laplacian and two parameters. Moreover, for the second nonlinear difference system with $(ϕ_1,ϕ_2)$-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.

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BibTeX RIS

Xingyong Zhang, Liben Wang. 2016-01-02. Multiple periodic solutions for two classes of nonlinear difference systems involving classical $(ϕ_1,ϕ_2)$-Laplacian. https://arxiv.org/abs/1601.00131

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