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On a difference equation with periodic coefficients. (English) Zbl 1121.39011

The paper concerns the difference equation \(x_n= \max\{A_n/x_{n-1}, B_n/x_{n-2}\}\) with positive \(k\)-periodic coefficients. In the case \(k= 2\) it is shown that every positive solution is eventually periodic with period 2, 3, 4 or 6. The case \(k= 3\) is also investigated.

MSC:

39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations
39A20 Multiplicative and other generalized difference equations
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References:

[1] DOI: 10.1016/S0898-1221(98)80040-0 · Zbl 0933.39030 · doi:10.1016/S0898-1221(98)80040-0
[2] Briden W.J., Proceedings of the Third International Conference on Difference Equations and Applications pp 49– (1999)
[3] Briden W.J., Communications on Applied Nonlinear Analysis 6 pp 31– (1999)
[4] Grove E.A., Fields Institute Communications 29 (2001)
[5] Grove E.A., Periodicities in Nonlinear Difference Equations (2005) · Zbl 1078.39009
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