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), 11331140
MSC (2000):
Primary 39A10, 39A11
Published electronically:
October 4, 2006
MathSciNet review:
2262916
Fulltext PDF Free Access
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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, WinstonSalem, North Carolina 27109
Email:
berenhks@wfu.edu
John D. Foley
Affiliation:
Department of Mathematics, Wake Forest University, WinstonSalem, 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:
http://dx.doi.org/10.1090/S0002993906085807
PII:
S 00029939(06)085807
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.
