On the Qualitative Analysis of Volterra IDDEs with Infinite Delay


Tunc O., KORKMAZ E., Atan Ö.

APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL, vol.15, no.1, pp.446-457, 2020 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 1
  • Publication Date: 2020
  • Title of Journal : APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL
  • Page Numbers: pp.446-457

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.