On the behaviors of solutions of systems of non-linear differential equations with multiple constant delays

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/s13398-021-01104-5
  • 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: Non-perturbed and perturbed systems of DDEs, UAS, Instability, Integrability, Boundedness, LKF, Constant delay, ASYMPTOTIC STABILITY, QUALITATIVE ANALYSES, BOUNDEDNESS, CRITERIA, MODEL
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this paper, non-perturbed and perturbed systems of non-linear differential equations with multiple constant delays are considered. Five new theorems on the qualitative properties of solutions, uniform asymptotic stability (UAS) and instability of trivial solution, boundedness and integrability of solutions, are obtained. The technique of the proofs is based on the construction of two new Lyapunov-Krasovskii functionals (LKFs). An advantage of the new LKFs used here is that they allow to eliminate the Gronwall's inequality and to obtain more convenient conditions. When we compare our results with the related results in the literature, the established conditions here are new, more convenient and general, less conservative, and they are more suitable for applications. We provide three examples to show the applications of the results of this paper.