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Boundedness character of positive solutions of a max difference equation. (English) Zbl 1116.39001

The difference equation \(y_n= \max(c,y_{n-k}/y_{n- m})\) with natural \(k\), \(m\), and positive initial values is considered. In the case \(c\geq 1\) every solution is bounded. In the case \(0< c< 1\) it is shown: If \(k\) is even then there exist unbounded solutions. If \(k\) is odd then there exists a special set of initial values such that all solutions are eventually periodic.

MSC:

39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations
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