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Nonlinear Analysis 66 (2007) 16331644 www.elsevier.com/locate/na
 

Summary: Nonlinear Analysis 66 (2007) 16331644
www.elsevier.com/locate/na
Global asymptotic behavior for delay dynamic equations
Douglas R. Anderson, Zackary R. Kenz
Department of Mathematics and Computer Science, Concordia College, Moorhead, MN 56562, USA
Received 3 September 2005; accepted 17 February 2006
Abstract
We give conditions under which the trivial solution of a first-order nonlinear variable-delay dynamic
equation is asymptotically stable, for arbitrary time scales that are unbounded above. In an example, we
apply our techniques to a logistic dynamic equation on isolated, unbounded time scales.
c 2006 Elsevier Ltd. All rights reserved.
MSC: 39A10; 34B10
Keywords: Time scales; Asymptotic behavior; Nonlinear equation; Delay
1. Nonlinear variable-delay dynamic equation
In the wake of Hilger's landmark paper [1], a rapidly expanding body of literature has sought
to unify, extend, and generalize ideas from discrete calculus, quantum calculus, and continuous
calculus to arbitrary time-scale calculus, where a time scale is simply any nonempty closed
set of real numbers. This paper illustrates this new understanding by extending some discrete
results from difference equations to dynamic equations on time scales. Henceforth we consider
the nonlinear variable delay dynamic equation

  

Source: Anderson, Douglas R. - Department of Mathematics and Computer Science, Concordia College

 

Collections: Mathematics