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The Scientific World Journal
Volume 2014 (2014), Article ID 965376, 7 pages
http://dx.doi.org/10.1155/2014/965376
Research Article

The Asymptotic Solutions for a Class of Nonlinear Singular Perturbed Differential Systems with Time delays

Science College, Linyi University, Linyi, Shandong 276005, China

Received 22 December 2013; Accepted 17 March 2014; Published 16 April 2014

Academic Editors: M. Han and Y. Xia

Copyright © 2014 Han Xu and Yinlai Jin. 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 study a kind of vector singular perturbed delay-differential equations. By using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and confirm the interior layer at . Meanwhile, on the basis of functional analysis skill, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved.