Periodic solutions to a difference equation with maximum
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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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Additional Information
- H. D. Voulov
- Affiliation: Department of Mathematics, Southern Illinois University at Carbondale, Carbondale, Illinois 62901-4408
- Email: voulovh@yahoo.com
- Received by editor(s): February 20, 2002
- Published electronically: November 13, 2002
- Communicated by: Carmen C. Chicone
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2155-2160
- MSC (2000): Primary 39A10
- DOI: https://doi.org/10.1090/S0002-9939-02-06890-9
- MathSciNet review: 1963762