Solution Expansions of the Quasiregular Cauchy Problem

Abstract

Consider a Cauchy problem

$$\frac{{dx}}{{dt}} = F(x,t,\varepsilon ,f(t,\varepsilon )),\,\,\,x{|_{t = 0}} = 0$$

((1.1))

. Here x ∈ R ^N, F ∈ R ^N are N-dimensional vectors, f ∈ R ^M is an M-dimensional vector, ε ∈ R is a small parameter, t ∈ R is an independent variable (time), R ^N is N-dimensional real space.