QUALITATIVE ANALYSIS OF INTEGRO-DIFFERENTIAL EQUATIONS WITH VARIABLE RETARDATION


Bohner M., Tunç O.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2021 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.3934/dcdsb.2021059
  • Title of Journal : DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
  • Keywords: Volterra RIDEs, stability, integrability, boundedness at infinity, Lyapunov-Krasovskii functional, ASYMPTOTIC STABILITY, SYSTEMS, DELAY, BOUNDEDNESS, POSITIVITY

Abstract

The paper is concerned with a class of nonlinear time-varying re-tarded integro-differential equations (RIDEs). By the Lyapunov-Krasovskii functional method, two new results with weaker conditions related to uniform stability (US), uniform asymptotic stability (UAS), integrability, boundedness, and boundedness at infinity of solutions of the RIDEs are given. For illustrative purposes, two examples are provided. The study of the results of this paper shows that the given theorems are not only applicable to time-varying linear RIDEs, but also applicable to time-varying nonlinear RIDEs.