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Zbl 1152.39308
Hamza, Alaa.E.; Khalaf-Allah, R.
On the recursive sequence $x_{n+1}=\frac{A\Pi^k_{i=l}x_{n-2i-1}}{B+C \Pi^{k-1}_{i=l}x_{n-2i}}$. (English)
[J] Comput. Math. Appl. 56, No. 7, 1726-1731 (2008). ISSN 0898-1221

Summary: The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $$x_{n+1}=\frac{A\Pi^k_{i=l}x_{n-2i-1}}{B+C \Pi^{k-1}_{i=l}x_{n-2i}},\qquad n=0,1,\ldots$$ where $A,B,C$ are nonnegative real numbers and $l,k$ are nonnegative integers, $l<k$. We discuss the existence of unbounded solutions under certain conditions when $l=0$.

MSC 2000:: *39A11 Stability of difference equations

Keywords: difference equation; periodic solution; globally asymptotically stable

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Zentralblatt MATH Berlin [Germany]