Advances in Difference Equations

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Delay dynamic equations with stability

  • Douglas R Anderson1Email author,
  • Robert J Krueger2 and
  • Allan C Peterson3
Advances in Difference Equations20062006:094051

https://doi.org/10.1155/ADE/2006/94051

©  Douglas R. Anderson et al. 2006

Received: 13 August 2005

Accepted: 23 October 2005

Published: 23 February 2006

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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Authors’ Affiliations

(1)
Department of Mathematics, Concordia College
(2)
Department of Mathematics, Concordia University
(3)
Department of Mathematics, University of Nebraska-Lincoln

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Copyright

© Douglas R. Anderson et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.