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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) Zbl 1152.39308
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 $l=0$.

39A11Stability of difference equations (MSC2000)
Full Text: DOI
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