On the Qualitative Analysis of Volterra IDDEs with Infinite Delay

Abstract

This investigation deals with a nonlinear Volterra integro-differential equation with infinite retardation (IDDE). We will prove three new results on the stability, uniformly stability (US) and square integrability (SI) of solutions of that IDDE. The proofs of theorems rely on the use of an appropriate Lyapunov-Krasovskii functional (LKF). By the outcomes of this paper, we generalize and obtain some former results in mathematical literature under weaker conditions.