Asymptotic behavior of solutions of Volterra integro-differential equations with and without retardation

Abstract

Asymptotic stability, uniform stability, integrability, and boundedness of solutions of Volterra integro-differential equations with and without constant retardation are investigated using a new type of Lyapunov–Krasovskii functionals. An advantage of the new functionals used here is that they eliminate using Gronwall’s inequality. Compared to related results in the literature, the conditions here are more general, simple, and convenient to apply. Examples to show the application of the theorems are included.