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)


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