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Global behavior of the max-type difference equation \(x_{n+1}=\max\{1/x_{n},A_{n}/x_{n - 1}\}\). (English) Zbl 1167.39303

Summary: We study global behavior of the following max-type difference equation \(x_{n+1}=\max\{1/x_{n},A_{n}/x_{n - 1}\}, n=0,1,\dots,\) where \(\{A_n\}_{n=0}^{\infty}\) is a sequence of positive real numbers with \(0\leq \text{inf} A_{n}\leq \text{sup} A_{n}<1\). The special case when \(\{A_n\}_{n=0}^{\infty}\) is a periodic sequence with period \(k\) and \(A_{n}\in (0,1)\) for every \(n\geq 0\) has been completely investigated by Y. Chen [J. Difference Equ. Appl. 11, No. 15, 1289–1294 (2005; Zbl 1086.39003)]. Here, we extend his results to the general case.

MSC:

39A11 Stability of difference equations (MSC2000)

Citations:

Zbl 1086.39003
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References:

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