Asymptotical Convergence of the Solutions of a Linear Differential Equation with Delays

Abstract

The asymptotic behavior of the solutions of the first-order differential equation containing delays is studied with , , , . The attention is focused on an analysis of the asymptotical convergence of solutions. A criterion for the asymptotical convergence of all solutions, characterized by the existence of a strictly increasing bounded solution, is proved. Relationships with the previous results are discussed, too.