## A note on the periodicity of the Lyness max equation.(English)Zbl 1149.39004

Summary: We investigate the periodic nature of solutions of a “max-type” difference equation sometimes referred to as the “Lyness max” equation. The equation we consider is $$x_{n+1}= \max\{x_n,A\}/x_{n-1}$$, where $$A$$ is a positive real parameter, $$x-1=A^{r_{-1}}$$, and $$x_0=A^{r_0}$$ such that $$r_{-1}$$ and $$r_0$$ are positive rational numbers. The results in this paper answer the open problem of E. A. Grove and G. Ladas [Periodicities in nonlinear difference equation, Boca Raton (FL) (2005; Zbl 1078.39009)].

### MSC:

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

Zbl 1078.39009
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### References:

 [1] doi:10.1016/S0022-247X(03)00587-0 · Zbl 1042.39002
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