On the rapidly decreasing solutions for some systems of differential equations with unbounded coefficients

Abstract

In this paper we continue the study of solvability of the non-homogeneous system of linear differential equations

$$y'(t) = C(t)y(t) + f(t),(y,f \in \mathbb{R}^n )$$

((1))

in the space of all rapidly decreasing functions, whereC(t) is a continuous square matrix of ordern for allt ∈ ℝ, whose elements are all unbounded functions on the real line ℝ. We give a necessary and sufficient condition in order that the system (1) be solvable in this space.