Averaging of initial-value and multipoint problems for oscillation systems with slowly varying frequencies and deviated argument

Abstract

We prove new theorems on the substantiation of the method of averaging over all fast variables on a segment and a semiaxis for multifrequency systems with deviated argument in slow and fast variables. An algorithm for the solution of a multipoint problem with parameters is studied, and an estimate for the difference of solutions of the original problem and the averaged problem is established.