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
- Proc. Amer. Math. Soc. 131 (2003), 905-909
- DOI: https://doi.org/10.1090/S0002-9939-02-06611-X
- Published electronically: July 17, 2002
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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.References
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Bibliographic 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