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Global Asymptotic Stability in a Class of Difference Equations

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. 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. 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

    MATH  MathSciNet  Article  Google Scholar 

  3. 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

    MATH  MathSciNet  Article  Google Scholar 

  4. 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

    MATH  MathSciNet  Article  Google Scholar 

  5. 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

    MATH  MathSciNet  Article  Google Scholar 

  6. 6.

    Kuang J: Applied Inequalities. Shandong Science and Technology Press, Jinan, China; 2004.

    Google Scholar 

  7. 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

    MATH  MathSciNet  Article  Google Scholar 

  8. 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 

Download references

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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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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation