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Journal of Difference Equations and Applications

Volume 14, 2008 - Issue 8
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Original Articles

Global asymptotic stability of a second order rational difference equation

Lin-Xia Hu Department of Mathematics , Tianshui Normal University , Tianshui, Gansu, 741001, People's Republic of China
, ,
Wan-Tong Li School of Mathematics and Statistics, Lanzhou University , Lanzhou, Gansu, 730000, People's Republic of China View further author information
&
Stevo Stević Mathematical Institute of the Serbian Academy of Science , Knez Mihailova 36/III, 11000, Beograd, Serbia Correspondencesstevic@ptt.rs sstevo@matf.bg.ac.yu
Pages 779-797
Received 10 May 2007
Accepted 26 Nov 2007
Published online: 12 Jun 2008
 
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Original Articles

Global asymptotic stability of a second order rational difference equation

Abstract

The main goal of the paper is to confirm Conjecture 9.5.5 stated by Kulenović and Ladas in Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures (Chapman & Hall/CRC, Boca Raton, FL, 2002). The boundedness, invariant intervals, semicycles and global attractivity of all nonnegative solutions of the equation are studied, where the parameters and the initial conditions are such that . It is shown that if the equation has no prime period-two solutions, then the unique positive equilibrium of the equation is globally asymptotically stable.

Keywords:

Notes

1 Supported by NSFC (No. 10571078) and NSF of Gansu Province of China (No. 3ZS061-A25-001).

Additional information

Notes on contributors

Wan-Tong Li

1

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