Center manifold method in the asymptotic integration problem for functional differential equations with oscillatory decreasing coeffcients. II

In this paper we study the asymptotic integration problem in the neighborhood of infnity for a certain class of linear functional differential systems. We construct the asymptotics for the solutions of the considered systems in a critical case. In the second part of the work we establish the existence of a critical manifold for the considered class of systems and study its main properties. We also investigate the asymptotic integration problem for a reduced system. We illustrate the proposed method with an example of constructing the asymptotics for the solutions of a certain scalar delay differential equation.