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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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Author information

Authors and 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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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., 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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  • DOI: https://doi.org/10.1155/ADE/2006/94051

Keywords

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