Advances in Difference Equations
Volume 2006 (2006), Article ID 94051, 19 pages
Delay dynamic equations with stability
1Department of Mathematics, Concordia College, Moorhead 56562, MN, USA
2Department of Mathematics, Concordia University, St. Paul 55104, USA
3Department of Mathematics, University of Nebraska-Lincoln, Lincoln 68588, NE, USA
Received 13 August 2005; Accepted 23 October 2005
Copyright © 2006 Douglas R. Anderson et al. 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.
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.