Averaging of Systems of Integro-Differential Equations with Multipoint Boundary Conditions

The paper considers a system of integro-differential equations with data rapidly oscillating over time and multipoint integral boundary conditions. The latter can explicitly depend on a large parameter $$\omega $$ —a high oscillation frequency of the original system of equations. For this problem, a limit problem at $$\omega \to \infty $$ is constructed and the passage to the limit is substantiated. Thus, for this problem, the paper justifies the method of time averaging, which is also called the Krylov–Bogolyubov averaging method.