Inequalities and stability for a linear scalar functional differential equation ✩,✩✩

There have been a lot of investigations about stability of the linear scalar functional differential equation x (t ) = a(t)x(t)+ b(t )x(t − h), where a, b :R+ →R continuous and h > 0 a constant. However, almost all investigations require a(t) 0 for asymptotic stability and a(t) 0 for instability. In this paper, we investigate Wazewski inequalities of solutions of the equation. As a consequence, we offer some sufficient conditions for asymptotic stability if a(t) 0 and instability if a(t) 0. In the case that a(t) and b(t ) are constant, we offer a region showing uniform asymptotic stability and instability of the zero solution of the equation. This region is different from J. Hale’s (1977).  2004 Elsevier Inc. All rights reserved