On the asymptotic integration of linear systems of differential equations with delay: MATHEMATICS. PHYSICS

An asymptotic representation of the solution for the basic initial problem of a system of linear singularly perturbed differential equations delay is constructed. The integration of such systems of equations with unstable spectrum was started in the works by M. I. Shkil’ and his students. In this study, an asymptotic representation of the solution of a system of differential-difference equations with instabilities in the spectrum of the main matrix is constructed. The instability peculiar only in equations with argument deviation is investigated. Asymptotic estimates of the error are given.