Sharp estimation for the solutions of inhomogeneous delay differential and Halanay type inequalities

Abstract

This paper is devoted to inhomogeneous Halanay-type inequalities together with inhomogeneous linear delay differential inequalities and equations. Based on the the variation of constants formula and some results borrowed from a recent paper of the authors, sharp conditions for the boundedness and the existence of the limit of the nonnegative solutions are established. The sharpness of the results are illustrated by examples and by comparison of results in some earlier works.

Keywords

• delay differential equation
• delay differential inequality
• halanay inequality