Justification of the Averaging Method for Multifrequency Systems with Pulse Action

We prove new estimates for the error of the averaging method for oscillation systems with slowly varying frequencies subjected to pulse action at fixed times. The main assumption is imposed not on all harmonics of the right-hand side of the system but only on resonance ones.__________Translated from Neliniini Kolyvannya, Vol. 8, No. 1, pp. 61–79, January–March, 2005.