On the periodicity of a max-type rational difference equation
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Authors
Changyou Wang
- School of Applied Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan 610225, P. R. China.
- College of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, P. R. China.
Xiaotong Jing
- College of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, P. R. China.
Xiaohong Hu
- College of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, P. R. China.
Rui Li
- College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, P. R. China.
Abstract
This paper shows that every well-defined solution of the following max-type difference equation
\[{x_{n + 1}} = \max \{ \frac{A}{{{x_n}}},\,\frac{A}{{{x_{n - 1}}}},\,{x_{n - 2}}\} ,\quad n \in {N_0},\]
where \(A \in R\) and the initial conditions \({x_{ - 2}},\,{x_{ - 1}},\,{x_0}\) are arbitrary non-zero real numbers is eventually periodic with period three by using new iteration method for the more general nonlinear difference equations and inequality skills as well as the mathematical induction. Our main results considerably improve results appearing in the literature.
Share and Cite
ISRP Style
Changyou Wang, Xiaotong Jing, Xiaohong Hu, Rui Li, On the periodicity of a max-type rational difference equation, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 9, 4648--4661
AMA Style
Wang Changyou, Jing Xiaotong, Hu Xiaohong, Li Rui, On the periodicity of a max-type rational difference equation. J. Nonlinear Sci. Appl. (2017); 10(9):4648--4661
Chicago/Turabian Style
Wang, Changyou, Jing, Xiaotong, Hu, Xiaohong, Li, Rui. "On the periodicity of a max-type rational difference equation." Journal of Nonlinear Sciences and Applications, 10, no. 9 (2017): 4648--4661
Keywords
- Max-type
- difference equation
- positive solution
- periodic solution.
MSC
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