Advances in Difference Equations
Volume 2006 (2006), Article ID 94051, 19 pages
doi:10.1155/ADE/2006/94051
Delay dynamic equations with stability
Douglas R. Anderson1
, Robert J. Krueger2
and Allan C. Peterson3
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
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.