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Zbl 1111.39003
Berenhaut, Kenneth S.; Stević, Stevo
The behaviour of the positive solutions of the difference equation $x_n = A + (\frac{x_{n-2}}{x_{n-1}})^p$.
(English)
[J] J. Difference Equ. Appl. 12, No. 9, 909-918 (2006). ISSN 1023-6198

For the difference equation in the title with positive parameters and $p\ne 1$ it is shown that there exist unbounded solutions if $p>1$, that all positive solutions converge to a 2-periodic solution it $(A+1)/2<p<1$, and that all solutions converge to $A+1$ in the other cases of $p$. The case $p=1$ was already treated by {\it A. M. Amleh, E. A. Grove, G. Ladas} and {\it D. A. Georgiou} [J. Math. Anal. Appl. 233, No. 2, 790--798 (1999; Zbl 0962.39004)].
[Lothar Berg (Rostock)]
MSC 2000:
*39A11 Stability of difference equations
39A20 Generalized difference equations

Keywords: rational difference equation; stability; boundedness; period two solution; unbounded solutions; positive solutions

Citations: Zbl 0962.39004

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