# Existence of periodic solutions for second-order nonlinear difference equations

Volume 9, Issue 4, pp 1505--1514 Publication Date: April 20, 2016
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### Authors

Zhiguo Ren - Department of Information Engineering, Jieyang Vocational and Technical College, Jieyang 522000, China. Jie Li - Quality Control Office, Zhongshan Torch College, Zhongshan 528436, China. Haiping Shi - Modern Business and Management Department, Guangdong Construction Vocational Technology Institute, Guangzhou 510440, China.

### Abstract

By using the critical point method, the existence of periodic solutions for second-order nonlinear difference equations is obtained. The proof is based on the Saddle Point Theorem in combination with variational technique. The problem is to solve the existence of periodic solutions of second-order nonlinear difference equations. One of our results obtained complements the result in the literature.

### Keywords

• Existence
• periodic solutions
• second-order
• nonlinear difference equations
• discrete variational theory.

•  39A23

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