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

Volume 10, Issue 8, pp 4381--4397 http://dx.doi.org/10.22436/jnsa.010.08.31

Publication Date: August 25, 2017 Submission Date: February 28, 2017

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Authors

Xingyong Zhang - Department of Mathematics, Faculty of Science, Kunming University of Science and Technology, Kunming, Yunnan 650500, P. R. China. Liben Wang - Department of Mathematics, Faculty of Science, Kunming University of Science and Technology, Kunming, Yunnan 650500, P. R. China.

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.

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Keywords

• Difference systems
• periodic solutions
• multiplicity
• variational approach.

MSC

•  39A23
•  37J45

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