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Zbl 1152.39012
Stević, Stevo
On the recursive sequence $x_{n+1} = \max \left\{ c, \frac {x_n^p}{x_{n-1}^p} \right\}$. (English)
[J] Appl. Math. Lett. 21, No. 8, 791-796 (2008). ISSN 0893-9659

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 $p,c\in(0,+\infty)$.\par 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 $p,c\in(0,1)$.
[Stefan Balint (Timişoara)]

MSC 2000:: *39A11 Stability of difference equations

Keywords: max type difference equations; boundedness; difference equation; global attractivity

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Zentralblatt MATH Berlin [Germany]