Averaging of integro-differential systems of equations with multipoint boundary conditions conditions

In this paper we consider a system of integro-differential equations with rapidly time oscillating data and multipoint integral boundary conditions. The latter may depend explicitly on a large parameter $\omega$ – high frequency of oscillations of the initial system of equations. For this problem the limit problem at $\omega\to\infty$ is constructed and the limit transition is justified. Thereby, the time averaging method, which is also called the Krylov–Bogoliubov averaging method, is justified for the above problem in this paper.