A change of variables in the asymptotic theory of differential equations with unbounded delays

In this paper, the author investigates the asymptotic properties of solutions of the nonhomogeneous linear differential equationẋ(t)=ax(τ(t))+bx(t)+f(t)with nonzero real scalars a,b and the unbounded lag. Using the change of the independent and dependent variable he relates the asymptotic behaviour of solutions of this equation to the asymptotic behaviour of solutions of auxiliary functional (nondifferential) equations.