On the fundamental qualitative properties of integro-delay differential equations

Bohner M., Tunç O., Korkmaz E.

Communications in Nonlinear Science and Numerical Simulation, vol.125, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 125
  • Publication Date: 2023
  • Doi Number: 10.1016/j.cnsns.2023.107320
  • Journal Name: Communications in Nonlinear Science and Numerical Simulation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Asymptotic stability (AS), Boundedness, Integrability, LKF, System of integro-delay differential equations, Uniform stability (US)
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

This paper discusses qualitative properties of solutions of certain unperturbed and perturbed systems of nonlinear integro-delay differential equations (IDDEs), namely asymptotic stability, uniform stability, integrability and boundedness. Here, four new theorems are proved on these properties of solutions by using Lyapunov–Krasovskiǐ functional (LKF) technique. As illustrations and applications of our results, we also provide two examples, solve them numerically, and plot the trajectories of their solutions. The results of this paper include weaker sufficient conditions than the ones found in the literature, e.g., some superfluous conditions are removed here, and the results have also new contributions to the qualitative theory of integro-differential equations (IDEs) and IDDEs.