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

 

On the oscillation and periodic character of a third order rational difference equation


Authors: W. T. Patula and H. D. Voulov
Journal: Proc. Amer. Math. Soc. 131 (2003), 905-909
MSC (2000): Primary 39A10
Published electronically: July 17, 2002
MathSciNet review: 1937429
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that every positive solution of the following difference equation:

\begin{displaymath}x_n = 1 + \frac{x_{n-2}}{x_{n-3}}, \quad n = 0,1,\ldots, \end{displaymath}

converges to a period two solution.


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Additional Information

W. T. Patula
Affiliation: Department of Mathematics, Southern Illinois University Carbondale, Carbondale, Illinois 62901-4408
Email: wpatula@math.siu.edu

H. D. Voulov
Affiliation: Department of Mathematics, Southern Illinois University Carbondale, Carbondale, Illinois 62901-4408
Email: voulovh@yahoo.com

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06611-X
PII: S 0002-9939(02)06611-X
Keywords: Periodic solution, semicycles, oscillation
Received by editor(s): May 28, 2001
Received by editor(s) in revised form: October 22, 2001
Published electronically: July 17, 2002
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2002 American Mathematical Society