Skip to main content

Oscillation of higher-order delay difference equations

Abstract

The oscillation and asymptotic behavior of the higher-order delay difference equation , n = 0,1,2,..., are investigated. Some sufficient conditions of oscillation and bounded oscillation of the above equation are obtained.

[1234567891012345678910]

References

  1. 1.

    Agarwal RP: Difference Equations and Inequalities. Theory, Methods, and Applications, Monographs and Textbooks in Pure and Applied Mathematics. Volume 228. 2nd edition. Marcel Dekker, New York; 2000:xvi+971.

    Google Scholar 

  2. 2.

    Cheng JF: Necessary and sufficient conditions for the oscillation of first-order functional difference equations. Journal of Biomathematics 2003,18(3):295–298.

    MathSciNet  Google Scholar 

  3. 3.

    Meng Q, Yan JR: Sufficient conditions for the oscillation of non-autonomous difference equations. Acta Mathematicae Applicatae Sinica 2002,18(2):325–332. 10.1007/s102550200032

    MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    Tang QG, Deng YB: Oscillation of difference equations with several delays. Journal of Hunan University 1998,25(2):1–3.

    MathSciNet  MATH  Google Scholar 

  5. 5.

    Tang XH, Yu JS: A further result on the oscillation of delay difference equations. Computers & Mathematics with Applications 1999,38(11–12):229–237. 10.1016/S0898-1221(99)00301-6

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Tang XH, Yu JS: Oscillation of delay difference equation. Computers & Mathematics with Applications 1999,37(7):11–20. 10.1016/S0898-1221(99)00083-8

    MathSciNet  Article  MATH  Google Scholar 

  7. 7.

    Tang XH, Yu JS: Oscillations of delay difference equations in a critical state. Applied Mathematics Letters 2000,13(2):9–15. 10.1016/S0893-9659(99)00158-5

    MathSciNet  Article  MATH  Google Scholar 

  8. 8.

    Tang XH, Zhang RY: New oscillation criteria for delay difference equations. Computers & Mathematics with Applications 2001,42(10–11):1319–1330. 10.1016/S0898-1221(01)00243-7

    MathSciNet  Article  MATH  Google Scholar 

  9. 9.

    Wang X: Oscillation of delay difference equations with several delays. Journal of Mathematical Analysis and Applications 2003,286(2):664–674. 10.1016/S0022-247X(03)00508-0

    MathSciNet  Article  MATH  Google Scholar 

  10. 10.

    Zhou Y: Oscillation and nonoscillation for difference equations with variable delays. Applied Mathematics Letters 2003,16(7):1083–1088. 10.1016/S0893-9659(03)90098-X

    MathSciNet  Article  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Yinggao Zhou.

Rights and permissions

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.

Reprints and Permissions

About this article

Cite this article

Zhou, Y. Oscillation of higher-order delay difference equations. Adv Differ Equ 2006, 065789 (2006). https://doi.org/10.1155/ADE/2006/65789

Download citation

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Asymptotic Behavior