Averaging of boundary-value problems for ordinary differential equations with slow and fast variables

The system x=X(t, x, y), y=Y(t, x, y) with slow and fast variables is considered. A theorem on the justification of the averaging method for the boundary-value problem R(x(0), x(T))=0, y(0)=y₀, is proved.Translated from Ukrainskii Maternaticheskii Zhurnal, Vol. 42, No. 9, pp. 1275–1278, September, 1990.