On the global behavior of the rational difference equation \(y_{n+1}=\frac{\alpha_n+y_{n-r}}{\alpha_n+y_{n-k}}\)

Authors : Sihem OUDİNA, Mohamed Amine KERKER, Abdelouahab SALMİ

Pages : 312-324

Doi:10.53006/rna.974156

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Publication Date : 2022-09-30

Article Type : Research Paper

Abstract :In this article, we study the global behavior of the following higher-order nonautonomous rational difference equation \[ y_{n+1}=\frac{\alpha_n+y_{n-r}}{\alpha_n+y_{n-k}},\quad n=0,1,..., \] where \insert ignore into journalissuearticles values(\left\{\alpha_n\right\}_{n\geq0}\); is a bounded sequence of positive numbers, \insert ignore into journalissuearticles values(k,r\); are nonnegative integers such that \insert ignore into journalissuearticles values(r Keywords : Rational difference equation, oscillation, local stability, global attractivity

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