Averaging of a normal system of ordinary differential equations of high frequency with a multipoint boundary value problem on a semi-axis

A multipoint boundary value problem for a nonlinear normal system of ordinary differential equations with a rapidly time-oscillating right-hand side is considered on a positive time semi-axis. For this problem, which depends on a large parameter (high oscillation frequency), a limiting (averaged) multipoint boundary value problem is constructed and a limiting transition in the Hölder space of bounded vector functions defined on the considered semi-axis is justified. Thus, for normal systems of differential equations in the case of a multipoint boundary value problem, the Krylov–Bogolyubov averaging method on the semi-axis is justified.