Klevchuk I. Investigation of the asymptotic behavior of solutions of functional differential equations.

The dissertation is devoted to the investigation of regularly and singularly perturbed functional differential equations with the help of integral manifolds method. New theorems on the existence of integral manifolds are proved. The reduction principle for investigating the stability of the zero solution of a nonlinear functional differential equations in the critical case is proved. The problem is reduced to investigating the zero solution of an ordinary differential equation constructed by the method of integral manifolds. A substitution is constructed which decomposed a nonlinear system of functional differential equations to the triangle-block form. It is shown that the system of linear functional differential equations can be splitted into two independent equations by a linear substitution.