Existence of Ψ-bounded solutions for a system of differential equations

Abstract

In this article, we present a necessary and sufficient condition for the existence of solutions to the linear nonhomogeneous system x' = A(t)x + ƒ(t). Under the condition stated, for every Lebesgue Ψ-integrable function ƒ there is at least one Ψ-bounded solution on the interval (0, +∞).