On the dynamics of a nonautonomous rational difference equation | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 17، دوره 12، شماره 1، مرداد 2021، صفحه 203-213 اصل مقاله (521.29 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.4760 | ||
| نویسندگان | ||
| Mohamed Amine Kerker* ؛ Elbahi Hadidi؛ Abdelouahab Salmi | ||
| Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, Annaba, 23000, Algeria | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| nonautonomous difference equation؛ global asymptotic stability؛ oscillation | ||
| مراجع | ||
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