The Asymptotic Bounds of Solutions of Linear Delay Systems

Our aim is to obtain conditions under which every solutionyof the vector functional differential equation[formula]can be estimated in terms of a solution ω of a scalar functional equation[formula]wherea(x) is a suitable real positive function andbis a suitable real negative constant. Moreover, ifB(x) is diagonal matrix, we derive more precise estimates ofyin terms of a solution ν of a vector functional equation[formula] where the elements ofA + (x) are formed by the absolute values of the corresponding elements ofA(x). These asymptotic results enable us to obtain sharp estimates of solutions of certain linear delay systems.