## 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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### References:

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