## 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 $$x_{n+1}= \max\{c,{x^p_n\over x^p_{n-1}}\}$$, $$n\in\mathbb{N}_0$$ with $$p,c\in(0,+\infty)$$.
It is shown that: (a) there exist unbounded solutions whenever $$p\geq 4$$; (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 $$c\geq 1$$; (d) all positive solutions converge to 1 whenever $$p,c\in(0,1)$$.

### MSC:

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

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