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On asymptotic behaviour of the difference equation x n+1 =α+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 =α+(x n-1 /x n ) p ,n=0,1,,

where α0 and p1.

MSC:
39A11Stability of difference equations (MSC2000)
39A20Generalized difference equations
References:
[1]A.M. Amleh, E.A. Grove, D.A. Georgion and G. Ladas, On the recursive sequence x n+1 =α+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=(α+βyn)/(γ+yn) Math. Sci. Res. Hot-Line 4,No 2. (2000), 1–11.
[3]V. L. Kocic, and G. Ladas,Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers, Dordrecht, 1993.
[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.
[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.