The global attractivity of the rational difference equation

Authors:
Kenneth S. Berenhaut, John D. Foley and Stevo Stevic

Journal:
Proc. Amer. Math. Soc. **135** (2007), 1133-1140

MSC (2000):
Primary 39A10, 39A11

Published electronically:
October 4, 2006

MathSciNet review:
2262916

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper studies the behavior of positive solutions of the recursive equation

with and , where . We prove that if , with odd, then tends to , exponentially. When combined with a recent result of E. A. Grove and G. Ladas (

*Periodicities in Nonlinear Difference Equations*, Chapman & Hall/CRC Press, Boca Raton (2004)), this answers the question when is a global attractor.

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Additional Information

**Kenneth S. Berenhaut**

Affiliation:
Department of Mathematics, Wake Forest University, Winston-Salem, North Carolina 27109

Email:
berenhks@wfu.edu

**John D. Foley**

Affiliation:
Department of Mathematics, Wake Forest University, Winston-Salem, North Carolina 27109

Email:
folejd4@wfu.edu

**Stevo Stevic**

Affiliation:
Mathematical Institute of Serbian Academy of Science, Knez Mihailova 35/I 11000 Beograd, Serbia

Email:
sstevic@ptt.yu, sstevo@matf.bg.ac.yu

DOI:
https://doi.org/10.1090/S0002-9939-06-08580-7

Keywords:
Difference equation,
stability,
exponential convergence,
periodic solution.

Received by editor(s):
September 7, 2005

Received by editor(s) in revised form:
November 11, 2005

Published electronically:
October 4, 2006

Additional Notes:
The first author acknowledges financial support from a Sterge Faculty Fellowship.

Communicated by:
Carmen C. Chicone

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.