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On the recursive sequence $x_{n+1} = \max \left\{ c, \frac {x_n^p}{x_{n-1}^p} \right\}$. (English) Zbl 1152.39012
This work studies the boundedness and global attractivity for the posivitive solutions of the difference equation $x_{n+1}= \max\{c,{x^p_n\over x^p_{n-1}}\}$, $n\in\bbfN_0$ with $p,c\in(0,+\infty)$. It is shown that: (a) there exist unbounded solutions whenever $p\ge 4$; (b) all positive solutions are bounded when $p\in(0, 4)$; (c) every positive solution is eventually equal to 1 when $p\in(0, 4)$ and $c\ge 1$; (d) all positive solutions converge to 1 whenever $p,c\in(0,1)$.

MSC:
39A11Stability of difference equations (MSC2000)
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References:
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