An application of Lyapunov-Razumikhin method to behaviors of Volterra integro-differential equations


Nieto J. J. , Tunç O.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, vol.115, no.4, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 115 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.1007/s13398-021-01131-2
  • Journal Name: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: VIDE, Stability, Lyapunov-Razumikhin method, Lyapunov function, FUNCTIONAL-DIFFERENTIAL EQUATIONS, ASYMPTOTIC STABILITY PROPERTIES, BOUNDEDNESS, SYSTEMS
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

This work presents some extensions and improvements of former results that allow proving asymptotic stability, uniform stability and global uniform asymptotic stability of zero solution to a class of non-linear Volterra integro-differential equations (VIDEs). Via the Lyapunov-Krasovskii and the Lyapunov-Razumikhin methods, three new results are proved on the mentioned concepts. These results are proved using Lyapunov functional and quadratic Lyapunov function. The results of this paper improve and extend the known ones in the literature. Some examples are given to validate these results and the concepts introduced.