@article {
author = {Kerker, Mohamed Amine and Hadidi, Elbahi and Salmi, Abdelouahab},
title = {On the dynamics of a nonautonomous rational difference equation},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {12},
number = {1},
pages = {203-213},
year = {2021},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2020.4760},
abstract = {In this paper, we study the following nonautonomous rational difference equation\[y_{n+1}=\frac{\alpha_n+y_n}{\alpha_n+y_{n-k}},\quad n=0,1,...,\]where $\left\{\alpha_n\right\}_{n\geq0}$ is a bounded sequence of positive numbers, $k$ is a positive integer and the initial values $y_{-k},...,y_0$ are positive real numbers. We give sufficient conditions under which the unique equilibrium $\bar{y}=1$ is globally asymptotically stable. Furthermore, we establish an oscillation result for positive solutions about the equilibrium point. Our work generalizes and improves earlier results in the literature.},
keywords = {nonautonomous difference equation,global asymptotic stability,oscillation},
url = {https://ijnaa.semnan.ac.ir/article_4760.html},
eprint = {https://ijnaa.semnan.ac.ir/article_4760_0bf826df007ba7d87c0c0452f01c321d.pdf}
}