On the qualitative analyses of integro-differential equations with constant time lag

Abstract

In this article, some new investigations are done on stability, asymptotically stability and instability of the zero solution and boundedness, integrability of solutions and integrability of derivatives of solutions of certain nonlinear Volterra delayed integrodifferential equations (DIDEs) by using the Lyapunov's functional method. To fulfill the aim of this work, three meaningful Lyapunov functionals are defined as main tools. Then, five new results are given on the mentioned qualitative properties of solutions of the considered DIDEs. Our results have contributions to the relevant literature and they have sufficient conditions. They include and improve some former results that can be found in [1].