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 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 1
  • Publication Date: 2020
  • Journal Name: APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL
  • Journal Indexes: Emerging Sources Citation Index
  • 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.