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Asymptotic 2-periodic difference equations with diagonally self-invertible responses. (English) Zbl 0963.39020

The author obtains sufficient conditions which guarantee that all positive solutions of a nonlinear equation \(x_{n+1}= f(x_n,x_{n-2})\) is asymptotically periodic with period 2.
For related results see the paper of G. Ladas [ibid. 2, No. 1, 97-99 (1996; Zbl 0853.39003)].

MSC:

39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations

Citations:

Zbl 0853.39003
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References:

[1] DOI: 10.1090/S0002-9939-98-04626-7 · Zbl 0904.39012 · doi:10.1090/S0002-9939-98-04626-7
[2] Karakostas G., Differential Equations and Dynamical systems 1 pp 289– (1993)
[3] Karakostas G., Greek Mathematical society pp 66– (1989)
[4] DOI: 10.1016/0362-546X(91)90192-4 · Zbl 0760.92019 · doi:10.1016/0362-546X(91)90192-4
[5] DOI: 10.1080/10236199608808079 · doi:10.1080/10236199608808079
[6] LaSalle J.P., CBMS Reg. Conf. Series in Applied mathematics 25 (1976)
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