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Boundedness and vanishing of solutions for a forced delay dynamic equation

Advances in Difference Equations volume 2006, Article number: 035063 (2006) Cite this article

Abstract

We give conditions under which all solutions of a time-scale first-order nonlinear variable-delay dynamic equation with forcing term are bounded and vanish at infinity, for arbitrary time scales that are unbounded above. A nontrivial example illustrating an application of the results is provided.

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References

  1. Anderson DR: Asymptotic behavior of solutions for neutral delay dynamic equations on time scales. Advances in Difference Equations 2006, 2006: 11 pages.

    Google Scholar 

  2. Anderson DR, Hoffacker J: Positive periodic time-scale solutions for functional dynamic equations. The Australian Journal of Mathematical Analysis and Applications 2006,3(1):1–14. article 5

    MathSciNet  MATH  Google Scholar 

  3. Anderson DR, Krueger RJ, Peterson AC: Delay dynamic equations with stability. Advances in Difference Equations 2006, 2006: 19 pages.

    MathSciNet  MATH  Google Scholar 

  4. Bohner M, Peterson A: Dynamic Equations on Time Scales, An Introduction with Applications. Birkhäuser Boston, Massachusetts; 2001:x+358.

    Book  MATH  Google Scholar 

  5. Bohner M, Peterson A (Eds): Advances in Dynamic Equations on Time Scales. Birkhäuser Boston, Massachusetts; 2003:xii+348.

    MATH  Google Scholar 

  6. Erbe LH, Xia H, Yu JS: Global stability of a linear nonautonomous delay difference equation. Journal of Difference Equations and Applications 1995,1(2):151–161. 10.1080/10236199508808016

    Article  MathSciNet  MATH  Google Scholar 

  7. Gopalsamy K, Kulenović MRS, Ladas G: Environmental periodicity and time delays in a "food-limited" population model. Journal of Mathematical Analysis and Applications 1990,147(2):545–555. 10.1016/0022-247X(90)90369-Q

    Article  MathSciNet  MATH  Google Scholar 

  8. Hilger S: Analysis on measure chains—a unified approach to continuous and discrete calculus. Results in Mathematics 1990,18(1–2):18–56.

    Article  MathSciNet  MATH  Google Scholar 

  9. Kocić VL, Ladas G: Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Mathematics and Its Applications. Volume 256. Kluwer Academic, Dordrecht; 1993:xii+228.

    MATH  Google Scholar 

  10. Kong Q, Sun Y, Zhang B: Nonoscillation of a class of neutral differential equations. Computers & Mathematics with Applications 2002,44(5–6):643–654. 10.1016/S0898-1221(02)00179-7

    Article  MathSciNet  MATH  Google Scholar 

  11. Kulenović MRS, Merino O: Discrete Dynamical Systems and Difference Equations with Mathematica. Chapman & Hall/CRC, Florida; 2002:xvi+344.

    Book  MATH  Google Scholar 

  12. Matsunaga H, Miyazaki R, Hara T: Global attractivity results for nonlinear delay differential equations. Journal of Mathematical Analysis and Applications 1999,234(1):77–90. 10.1006/jmaa.1999.6325

    Article  MathSciNet  MATH  Google Scholar 

  13. Qian C, Sun Y: Global attractivity of solutions of nonlinear delay differential equations with a forcing term. to appear in Nonlinear Analysis

  14. Zhang X, Yan J: Global asymptotic behavior of nonlinear difference equations. Computers & Mathematics with Applications 2005,49(9–10):1335–1345. 10.1016/j.camwa.2005.01.017

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Concordia College, Moorhead, MN, 56562, USA

    Douglas R Anderson

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  1. Douglas R Anderson
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Correspondence to Douglas R Anderson.

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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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Anderson, D.R. Boundedness and vanishing of solutions for a forced delay dynamic equation. Adv Differ Equ 2006, 035063 (2006). https://doi.org/10.1155/ADE/2006/35063

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  • DOI: https://doi.org/10.1155/ADE/2006/35063

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