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Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 38769, 13 pages
http://dx.doi.org/10.1155/JAMSA/2006/38769

Robustness of solutions of linear differential equations with infinite delay

Department of Mathematics and Statistics, Mu'tah University, Mu'tah 61710, Jordan

Received 22 November 2004; Revised 28 June 2005; Accepted 4 August 2005

Copyright © 2006 Anwar A. Al-Badarneh (Al-Nayef) and Rabaa K. Maaitah. 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.

Abstract

We use some consequences of the concept of semihyperbolicity of the solution operator to show robustness of solutions of the linear delay differential equation x(t)=Ax(t)+Bx(tr) with infinite delay with respect to a small nonlinear perturbation.