Asymptotic equivalence of linear differential systems to systems with infinitely differentiable coefficients

Abstract

t was shown in [1–3] that a linear system of differential equations can be replaced by a linear system with infinitely differentiable coefficients with preservation of certain asymptotic properties of solutions. The aim of the present paper is to show that, for each linear system with bounded locally integrable coefficients, there exists an equivalent (in the sense of Lyapunov transformations) linear system with infinitely differentiable coefficients that have bounded derivatives of arbitrary order on the half-line [0, +∞).