Averaging of a Normal System of Ordinary Differential Equations of High Frequency with a Multipoint Boundary Value Problem on a Semiaxis

Abstract

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 semiaxis. 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 semiaxis 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 semiaxis is justified.