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Delay dynamic equations with stability

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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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