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.
Tunç, Osman; Korkmaz, Erdal; and Atan, Özkan
On the Qualitative Analysis of Volterra IDDEs with Infinite Delay,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 15,
1, Article 25.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss1/25