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

Robustness of solutions of linear differential equations with infinite delay

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

 Department of Mathematics and Statistics, Mu'tah University, Mu'tah 61710, Jordan
Received 22 November 2004; Revised 28 June 2005; Accepted 4 August 2005

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(t−r) with infinite delay with respect to a small nonlinear perturbation.