Averaging in Boundary-Value Problems for Systems of Differential and Integrodifferential Equations

The averaging method is applied to the investigation of the problem of existence of solutions of boundary-value problems for systems of differential and integrodifferential equations. It is shown that if the averaged boundary-value problem has a solution, then the original problem also has a solution. Note that, in this case, the system obtained as a result of averaging of a system of integrodifferential equations has the form of a simpler system of ordinary differential equations.