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On the recursive sequence ${x}_{n+1}=\frac{A{{\Pi }}_{i=l}^{k}{x}_{n-2i-1}}{B+C{{\Pi }}_{i=l}^{k-1}{x}_{n-2i}}$. (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

${x}_{n+1}=\frac{A{{\Pi }}_{i=l}^{k}{x}_{n-2i-1}}{B+C{{\Pi }}_{i=l}^{k-1}{x}_{n-2i}},\phantom{\rule{2.em}{0ex}}n=0,1,...$

where $A,B,C$ are nonnegative real numbers and $l,k$ are nonnegative integers, $l. We discuss the existence of unbounded solutions under certain conditions when $l=0$.

##### MSC:
 39A11 Stability of difference equations (MSC2000)
##### References:
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