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Delay dynamic equations with stability

Advances in Difference Equations volume 2006, Article number: 094051 (2006) Cite this article

Abstract

We first give conditions which guarantee that every solution of a first order linear delay dynamic equation for isolated time scales vanishes at infinity. Several interesting examples are given. In the last half of the paper, we give conditions under which the trivial solution of a nonlinear delay dynamic equation is asymptotically stable, for arbitrary time scales.

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References

  1. 1.

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

    Google Scholar 

  2. 2.

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

    Google Scholar 

  3. 3.

    Haddock JR, Kuang Y: Asymptotic theory for a class of nonautonomous delay differential equations. Journal of Mathematical Analysis and Applications 1992,168(1):147–162. 10.1016/0022-247X(92)90195-J

    MathSciNet  Article  MATH  Google Scholar 

  4. 4.

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

    MathSciNet  Article  MATH  Google Scholar 

  5. 5.

    Kac V, Cheung P: Quantum Calculus, Universitext. Springer, New York; 2002:x+112.

    Google Scholar 

  6. 6.

    Kelley WG, Peterson AC: The Theory of Differential Equations, Classical and Qualitative. Pearson Prentice Hall, New Jersey; 2004.

    Google Scholar 

  7. 7.

    Kuang Y: Delay Differential Equations with Applications in Population Dynamics, Mathematics in Science and Engineering. Volume 191. Academic Press, Massachusetts; 1993:xii+398.

    Google Scholar 

  8. 8.

    Ladde GS, Lakshmikantham V, Zhang BG: Oscillation Theory of Differential Equations with Deviating Arguments, Monographs and Textbooks in Pure and Applied Mathematics. Volume 110. Marcel Dekker, New York; 1987:vi+308.

    Google Scholar 

  9. 9.

    Raffoul Y: Stability and Periodicity in Completely Delayed Equations. to appear in Journal of Mathematical Analysis and Applications

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Author information

Affiliations

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

    Douglas R Anderson

  2. Department of Mathematics, Concordia University, St. Paul, 55104, USA

    Robert J Krueger

  3. Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, 68588, USA

    Allan C Peterson

Authors
  1. Douglas R Anderson
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  2. Robert J Krueger
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  3. Allan C Peterson
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Corresponding author

Correspondence to Douglas R Anderson.

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Anderson, D.R., Krueger, R.J. & Peterson, A.C. Delay dynamic equations with stability. Adv Differ Equ 2006, 094051 (2006). https://doi.org/10.1155/ADE/2006/94051

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Keywords

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