## Periodic solutions to a difference equation with maximum.(English)Zbl 1019.39005

Consider the difference equation $x_n=\max \left\{ \frac A{x_{n-1}},\;\frac B{x_{n-3}},\frac C{x_{n-5}}\right\} n=0,1,\dots,\tag{$$*$$}$ where $$A,B,C$$ are any nonnegative real numbers with $$A+B+C>0.$$ The author proves that there exists a positive integer $$T$$ such that every positive solution of $$(*)$$is eventually periodic of period $$T$$. The period $$T$$ $$\in \{2,6,8,10\}$$ and is determined according to the values of $$A$$ , $$B$$ and $$C$$.
Reviewer: Fozi Dannan (Doha)

### MSC:

 39A11 Stability of difference equations (MSC2000) 39B05 General theory of functional equations and inequalities

### Keywords:

periodic solutions; nonlinear difference equation
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### References:

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