THE EXTENSION OF THE AVERAGING THEORY ONTO DIFFERENTIAL EQUATIONS WITH LARGE-AMPLITUDE QUICKLY OSCILLATING TERMS. THE PROBLEM ON PERIODIC SOLUTIONS

摘要

In the main theorems of the classic N.N. Bogolubov averaging theory [1] one considers systems of ordinary differential equations in the so-called standard form, i. e., representable in the form dx/dt=f(x,ωt), (0.1) where the vector-function f(x, τ) has the average value with respect to r, and w is a large parameter.