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On the periodicity of a difference equation with maximum. (English) Zbl 1149.39005

Summary: We investigate the periodic nature of solutions of the max difference equation
\[ x_{n+1}= \max\{x_n,A\}/(x_nx_{n-1}), \quad n=0,1,\dots, \] where \(A\) is a positive real parameter, and the initial conditions \(x_{-1}=A^{r_{-1}}\) 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 6.2 posed by E. A. Grove and G. Ladas in their book “Periodicities in nonlinear difference equations”. Boca Raton (FL) (2005; Zbl 1078.39009).

MSC:

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

Citations:

Zbl 1078.39009
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References:

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