New Results on the Qualitative Analysis of Solutions of Vides by the Lyapunov-Razumikhin Technique

A new mathematical model described by a Volterra integrodifferential 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. They can be also regarded as nonlinear generalizations of these results. Moreover, they are weaker than some available results cited in the bibliography. Two examples are presented to demonstrate possible applications of these results and the introduced concepts. The application of the Lyapunov-Razumikhin technique leads to a significant difference and gives certain advantages over the related methods used in the books and papers cited in the bibliography