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On asymptotic behaviour of the difference equation $x_{n+1} = \alpha+\frac{x_{n-1}^p}{x_n^p}$. (English) Zbl 1052.39005
The authors investigate the oscillation with respect to the equilibrium, and the asymptotic behaviour of the positive solutions to the difference equation $$ x_{n+1}=\alpha+(x_{n-1}/x_n)^p,\, n=0,1,\dots, $$ where $\alpha\geq 0$ and $p\geq 1$.

39A11Stability of difference equations (MSC2000)
39A20Generalized difference equations
Full Text: DOI
[1] A.M. Amleh, E.A. Grove, D.A. Georgion and G. Ladas, On the recursive sequence $x_{n + 1} = \alpha + \frac{{x_{n - 1} }}{{x_n }}$ , J. Math. Anal. Appl. 233, (1999), 790--798. · Zbl 0962.39004 · doi:10.1006/jmaa.1999.6346
[2] C. Gibbons, M. Kulenović and G. Ladas,On the recursive sequence y n+1=({$\alpha$}+{$\beta$}yn)/({$\gamma$}+yn) Math. Sci. Res. Hot-Line 4,No 2. (2000), 1--11. · Zbl 1039.39004
[3] V. L. Kocic, and G. Ladas,Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers, Dordrecht, 1993. · Zbl 0787.39001
[4] V.L. Kocic, G. Ladas and I. Rodrigues,On the rational recursive sequences, J. Math. Anal. Appl. 173 (1993), 127--157. · Zbl 0777.39002 · doi:10.1006/jmaa.1993.1057
[5] W. Kosmala, M. Kulenović, G. Ladas and C. Teixeira,On the recursive sequence, y n+1= (p+yn)/(qyn+yn), J. Math. Anal. Appl. 251, (2000), 571--586. · Zbl 0967.39004 · doi:10.1006/jmaa.2000.7032
[6] Z. Zhang, B. Ping and W. Dong,Oscillatory of unstable type second-order neutral difference equations, Journal of Applied Mathematics and computing 9,No 1(2002), 87--100. · Zbl 0999.39014
[7] Z. Zhou, J. Yu and G. Lei,O scillations for even-order neutral difference equations, Journal of Applied Mathematics and Computing(old:KJCAM) 7, No 3(2000), 601--610. · Zbl 0966.39004