New results on the qualitative analysis of solutions of VIDEs by the Lyapunov–Razumikhin technique

Osman Tunç; E.  Korkmaz

doi:10.37863/umzh.v74i11.6083

Osman Tunç Van Yuzuncu Yil Univ., Turkey https://orcid.org/0000-0003-2965-4561
E. Korkmaz Muş Alparslan Univ., Turkey

DOI: https://doi.org/10.37863/umzh.v74i11.6083

Keywords: VIDDE, UAS, boundedness, square integrability, LRT, fixed constant delay.

Abstract

UDC 517.9

A new mathematical model described by a Volterra integro-differential equation (VIDE) with constant delay is examined. New agreeable conditions on the uniformly asymptotic stability, boundedness, and square integrability of solutions of the VIDE are obtained by using the Lyapunov–Razumikhin technique. The established conditions improve some former results and they are also nonlinear generalizations of these results. Moreover, they are weaker than some available results cited in the bibliography of this paper. Two examples are presented to demonstrate applications of these results and the introduced concepts. The use of the Lyapunov–Razumikhin technique leads to a significant difference and gives an advantage over the related methods used in the books and papers cited in the bibliography.

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