Qualitative Properties in Nonlinear Volterra Integro-Differential Equations With Delay

Abstract

This paper considers a class of scalar and vector nonlinear Volterra integro-differential equations of the first order with a constant delay. We demonstrate the stability, uniform stability, boundedness, convergence and square integrability of the solutions. The technique of proof involves defining appropriate Lyapunov functionals. Our results improve the results obtained in the literature. (C) 2016 The Author. Production and hosting by Elsevier B.V. on behalf of Taibah University.