Danylyuk I. Justification of the asymptotic methods for the multifrequency systems with the deviated argument

This thesis is devoted to the multifrequency oscillatory systems with delay. In this work has been investigated the method of averaging over all fast variables for multifrequency oscillatory systems with delay in fast and slow variables. The estimate of solutions difference between initial and averaged problems has been established. The solveability of boundary value problems for multifrequency systems with delay using averaging method has been investigated. The value of solutions difference also has been established. We found the existence conditions of the integral manifold of multifrequency nonlinear oscillatory system with delay and investigated it's properties.