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Fourth International Conference on Neural, Parallel & Scientific Computations
August 11-14, 2010
Morehouse College
Atlanta, Georgia, USA |
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Organizers
M. Sambandham and IFNA
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Shift Operators and Stability in Delayed Dynamic Equations
by
Murat Adivar
Izmir Universtiy of Economics, Department of Mathematics, 35330 Balcova, Izmir TURKEY
Coauthors: YOUSSEF N. RAFFOUL
Abstract
In this paper, we make use of the shift operators that were introduced by the authors in a previous paper,
so that general delay dynamic equation of the form
|
xD(t)=a(t)x(t)+b(t)x(d-(h, t))d-D(h, t), t ∈ [t0, ∞)T |
|
can be analyzed with respect to stabilities and existence of solutions.
Thus, we will use Lyapunov's direct method to obtain inequalities that lead
to stability and instability. Therefore, as a direct consequence of our shift operators,
we obtain new stability conditions for delay differential, delay difference, and delay q-difference equations
which are particular cases of our delay dynamic equation. Finally, we compare
our results to the ones in the existing literature to show how we improve them.
Date received: April 18, 2010
Copyright © 2010 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # cbas-27.