Non-linear differential equations of higher order

In this article we study the problem of the existence of periodic solutions of the perturbed differential equations of higher order. These theorems were inspired by the work of V.I. Zubov and associated with such notions as asymptotically stability in the large and stability in the Dirichlet's sense in the large. Proofs of these theorems have a topological sense. We consider periodically perturbed autonomous system of the ordinary differential equations and denote the sufficient conditions of the existence of periodic solution.