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.
Kerker, M., Hadidi, E., Salmi, A. (2020). On the dynamics of a nonautonomous rational difference equation. International Journal of Nonlinear Analysis and Applications, 12(1), 203-213. doi: 10.22075/ijnaa.2020.4760
MLA
Mohamed Amine Kerker; Elbahi Hadidi; Abdelouahab Salmi. "On the dynamics of a nonautonomous rational difference equation". International Journal of Nonlinear Analysis and Applications, 12, 1, 2020, 203-213. doi: 10.22075/ijnaa.2020.4760
HARVARD
Kerker, M., Hadidi, E., Salmi, A. (2020). 'On the dynamics of a nonautonomous rational difference equation', International Journal of Nonlinear Analysis and Applications, 12(1), pp. 203-213. doi: 10.22075/ijnaa.2020.4760
VANCOUVER
Kerker, M., Hadidi, E., Salmi, A. On the dynamics of a nonautonomous rational difference equation. International Journal of Nonlinear Analysis and Applications, 2020; 12(1): 203-213. doi: 10.22075/ijnaa.2020.4760
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