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

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 att=σ. Meanwhile, on the basis of functional analysis skill, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved.