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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the oscillation and periodic character of a third order rational difference equation
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by W. T. Patula and H. D. Voulov PDF
Proc. Amer. Math. Soc. 131 (2003), 905-909 Request permission

Abstract:

We prove that every positive solution of the following difference equation: \[ x_n = 1 + \frac {x_{n-2}}{x_{n-3}}, \quad n = 0,1,\ldots , \] 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
  • 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
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 905-909
  • MSC (2000): Primary 39A10
  • DOI: https://doi.org/10.1090/S0002-9939-02-06611-X
  • MathSciNet review: 1937429