Asymptotic solutions of the initial value problem for a degenerated singularly perturbed system of differential equations with retarded argument (Q2901699)

A class of singularly perturbed linear systems with retarded argument is considered. To study the solvability of the initial-value problem, the author uses the reduction of the degenerated system to its canonical form. The time-varying matrices of the system considered admit expansions in power series with respect to the small parameter. It is proved that the solution of the initial value problem is unique provided that extra conditions on the elementary divisors of the associated matrix pencil hold. An expansion of the solution in power series of the small parameter is obtained on the interval corresponding to the delay parameter. The prolongation of such an expansion to subsequent time-intervals is presented as well.