Periodic solutions to a difference equation with maximum

Voulov, H.

doi:10.1090/S0002-9939-02-06890-9

Periodic solutions to a difference equation with maximum
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by H. D. Voulov PDF

Proc. Amer. Math. Soc. 131 (2003), 2155-2160 Request permission

Abstract:

An open problem posed by G. Ladas is to investigate the difference equation \[ x_n=\max \left \{\frac {A}{x_{n-1}} ,\frac {B}{x_{n-3}} ,\frac {C} {x_{n-5}}\right \},\quad n=0,1,\ldots ,\] where $A, B, C$ are any nonnegative real numbers with $A+B+C > 0$. We prove that there exists a positive integer $T$ such that every positive solution of this equation is eventually periodic of period $T$.

References

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