Existence of Ψ-bounded solutions for nonhomogeneous linear differential equations

Abstract

In this article we present a necessary and sufficient condition for the existence of ψ-bounded solution on ℝ of the nonhomogeneous linear differential equation x′ = A(t)x + ƒ(t). We associate that with the condition of the concept ψ-dichotomy on ℝ of the homogeneous linear differential equation x′ = A(t)x.