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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Periodic solutions to a difference equation with maximum


Author: H. D. Voulov
Journal: Proc. Amer. Math. Soc. 131 (2003), 2155-2160
MSC (2000): Primary 39A10
Published electronically: November 13, 2002
MathSciNet review: 1963762
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Abstract | References | Similar Articles | Additional Information

Abstract: An open problem posed by G. Ladas is to investigate the difference equation

\begin{displaymath}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,\end{displaymath}

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 [Enhancements On Off] (What's this?)

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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

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06890-9
PII: S 0002-9939(02)06890-9
Keywords: Periodic solutions, nonlinear difference equations
Received by editor(s): February 20, 2002
Published electronically: November 13, 2002
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2002 American Mathematical Society