Open Access

Global Asymptotic Stability in a Class of Difference Equations

Advances in Difference Equations20082007:016249

https://doi.org/10.1155/2007/16249

Received: 29 April 2007

Accepted: 5 November 2007

Published: 22 January 2008

Abstract

We study the difference equation , , , where and are all continuous functions, and We prove that this difference equation admits as the globally asymptotically stable equilibrium. This result extends and generalizes some previously known results.

[12345678]

Authors’ Affiliations

(1)
College of Computer Science, Chongqing University
(2)
School of Computer and Information, Chongqing Jiaotong University
(3)
Department of Computer Science, Hong Kong Baptist University

References

  1. Ladas G: Open problems and conjectures. Journal of Difference Equations and Applications 1996,2(4):449–452. 10.1080/10236199608808079View ArticleGoogle Scholar
  2. Sun T, Xi H: Global attractivity for a family of nonlinear difference equations. Applied Mathematics Letters 2007,20(7):741–745. 10.1016/j.aml.2006.08.024MATHMathSciNetView ArticleGoogle Scholar
  3. Kruse N, Nesemann T: Global asymptotic stability in some discrete dynamical systems. Journal of Mathematical Analysis and Applications 1999,235(1):151–158. 10.1006/jmaa.1999.6384MATHMathSciNetView ArticleGoogle Scholar
  4. Nesemann T: Positive nonlinear difference equations: some results and applications. Nonlinear Analysis: Theory, Methods & Applications 2001,47(7):4707–4717. 10.1016/S0362-546X(01)00583-1MATHMathSciNetView ArticleGoogle Scholar
  5. Yang X, Evans DJ, Megson GM: Global asymptotic stability in a class of Putnam-type equations. Nonlinear Analysis: Theory, Methods & Applications 2006,64(1):42–50. 10.1016/j.na.2005.06.005MATHMathSciNetView ArticleGoogle Scholar
  6. Kuang J: Applied Inequalities. Shandong Science and Technology Press, Jinan, China; 2004.Google Scholar
  7. Berenhaut KS, Stević S: The global attractivity of a higher order rational difference equation. Journal of Mathematical Analysis and Applications 2007,326(2):940–944. 10.1016/j.jmaa.2006.02.087MATHMathSciNetView ArticleGoogle Scholar
  8. Xi H, Sun T: Global behavior of a higher-order rational difference equation. Advances in Difference Equations 2006, 2006: 7 pages.View ArticleGoogle Scholar

Copyright

© Xiaofan Yang et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.