On the Fundamental Qualitative Properties of Integro-Delay Differential Equations

Abstract

This paper discusses qualitative properties of solutions of certain unperturbed and perturbed systems of nonlinear integro-delay differential equations (IDDEs), namely asymptotic stability, uniform stability, integrability and boundedness. Here, four new theorems are proved on these properties of solutions by using Lyapunov-Krasovskii? functional (LKF) technique. As illustrations and applications of our results, we also pro-vide two examples, solve them numerically, and plot the trajectories of their solutions. The results of this paper include weaker sufficient conditions than the ones found in the literature, e.g., some superfluous conditions are removed here, and the results have also new contributions to the qualitative theory of integro-differential equations (IDEs) and IDDEs.(C) 2023 Elsevier B.V. All rights reserved.