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On the difference equation $y_{n+1}=A + \frac {y_n}{y_{n-k}}$ with $A < 0$. (English) Zbl 1096.39011
For the difference equation in the title the global asymptotic stability of the equilibrium $A+1$ is studied.

39A11Stability of difference equations (MSC2000)
39A20Generalized difference equations
Full Text: DOI
[1] Abu-Saris, R.; Devault, R.: Global stability of yn+1=A+ynyn-k. Appl. math. Lett. 16, 173-178 (2003) · Zbl 1049.39002
[2] Amleh, A.; Grove, E.; Ladas, G.; Georgiou, G.: On the recursive sequence $xn+1=\alpha +xn-1xn$. J. math. Anal. appl. 533, 790-798 (1999) · Zbl 0962.39004
[3] Devault, R.; Schultz, S. W.; Ladas, G.: On the recursive sequence xn+1=Axn+1xn-2. Proc. am. Math. soc. 126, 3257-3261 (1998) · Zbl 0904.39012
[4] Devault, R.; Kosmala, W.; Ladas, G.; Schultz, S. W.: On the recursive sequence global behavior of yn+1=p+yn-kqyn+yn-k. Nonlinear anal. 47, 4743-4751 (2001) · Zbl 1042.39523
[5] El-Owaidy, H.; Ahmed, A.; Mousa, M.: On asymptotic behaviour of the difference equation $x$n+1=\alpha +xn-kxn. Appl. math. Comp. 147, 163-167 (2004) · Zbl 1042.39001
[6] Kocic, V. L.; Ladas, G.: Global asymptotic behavior of nonlinear difference equations of higher. (1993) · Zbl 0787.39001
[7] Kosmala, W.; Kulenovic, M. R. S.; Ladas, G.; Teixeira, C. T.: On the recursive sequence yn+1=p+yn-1qyn+yn-1. J. math. Anal. appl. 251, 571-586 (2000) · Zbl 0967.39004
[8] Kuruklis, S. A.: The asymptotic stability of xn+1-axn+bxn-k=0. J. math. Anal. appl. 188, 719-731 (1994) · Zbl 0842.39004
[9] Papanicolaou, V. G.: On the asymptotic stability of a class of linear difference equations. Math. mag. 69, 34-43 (1996) · Zbl 0866.39001
[10] M. Saleh, M. Aloqeili, On the rational difference equation yn+1=A+yn-kyn, Appl. Math. Comput., in press, doi:10.1016/j.amc.2005.01.094.