Stability tests and solution estimates for non-linear differential equations

Tunç O.

International Journal of Optimization and Control: Theories and Applications, cilt.13, sa.1, ss.92-103, 2023 (Scopus) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 1
  • Basım Tarihi: 2023
  • Doi Numarası: 10.11121/ijocta.2023.1251
  • Dergi Adı: International Journal of Optimization and Control: Theories and Applications
  • Derginin Tarandığı İndeksler: Scopus, Academic Search Premier, Communication Abstracts, zbMATH, Directory of Open Access Journals, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.92-103
  • Anahtar Kelimeler: Delay differential equations, Ordinary differential equations, Lyapunov-Krasovski??functional method, Second method of Lyapunov
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

© 2023 Balikesir University. All rights reserved.This article deals with certain systems of delay differential equations (DDEs) and a system of ordinary differential equations (ODEs). Here, five new theorems are proved on the fundamental properties of solutions of these systems. The results on the properties of solutions consist of sufficient conditions and they dealt with uniformly asymptotically stability (UAS), instability and integrability of solutions of unperturbed systems of DDEs, boundedness of solutions of a perturbed system of DDEs at infinity and exponentially stability (ES) of solutions of a system of nonlinear ODEs. Here, the techniques of proofs depend upon the Lyapunov- Krasovskiĭ functional (LKF) method and Lyapunov function (LF) method. For illustrations, in particular cases, four examples are constructed as applications. Some results of this paper are given at first time in the literature, and the other results generalize and improve some related ones in the literature.