Danylyuk I. M.
Averaging of initial-value and multipoint problems for oscillation systems with slowly varying frequencies and deviated argument
Ukr. Mat. Zh. - 2007. - 59, № 3. - pp. 412–430
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.