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Global Asymptotic Stability in a Class of Difference Equations

Advances in Difference Equations volume 2007, Article number: 016249 (2008) Cite this article

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.

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References

  1. Ladas G: Open problems and conjectures. Journal of Difference Equations and Applications 1996,2(4):449–452. 10.1080/10236199608808079

    Article  Google 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.2006.08.024

    Article  MATH  MathSciNet  Google 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.1999.6384

    Article  MATH  MathSciNet  Google 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)00583-1

    Article  MATH  MathSciNet  Google 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.2005.06.005

    Article  MATH  MathSciNet  Google 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.2006.02.087

    Article  MATH  MathSciNet  Google Scholar 

  8. Xi H, Sun T: Global behavior of a higher-order rational difference equation. Advances in Difference Equations 2006, 2006: 7 pages.

    Article  Google Scholar 

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Authors and Affiliations

  1. College of Computer Science, Chongqing University, Chongqing, 400044, China

    Xiaofan Yang & Yuan Yan Tang

  2. School of Computer and Information, Chongqing Jiaotong University, Chongqing, 400074, China

    Xiaofan Yang & Jianqiu Cao

  3. Department of Computer Science, Hong Kong Baptist University, Kowloon, Hong Kong

    Limin Cui & Yuan Yan Tang

Authors
  1. Xiaofan Yang
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  2. Limin Cui
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  3. Yuan Yan Tang
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  4. Jianqiu Cao
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Correspondence to Xiaofan Yang.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Yang, X., Cui, L., Tang, Y.Y. et al. Global Asymptotic Stability in a Class of Difference Equations. Adv Differ Equ 2007, 016249 (2008). https://doi.org/10.1155/2007/16249

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

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