Asymptotic convergence of formal solutions of linear systems of differential equations with slowly varying coefficients (Q1112998)

The object of study in this paper is a linear system of differential equations with slowly varying coefficients of the form \(dx/dt=A(\tau,\epsilon)x(1)\). Here \(\rho =\epsilon t\), \(\epsilon\) is a small real parameter, \(x\in R^ n\) and the characteristic equation of the matrix A(\(\tau\),0) has an nth root \(\lambda_ 0(\tau)\), to which a root subspace of dimension n corresponds. The formal solutions of the system (1) are constructed and asymptotic convergence of these solutions to the corresponding exact solutions of the system (1) under more weak conditions is proved.