On The Fundamental Qualitative Properties Of Integro-delay Differential Equations
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.
M. Bohner et al., "On The Fundamental Qualitative Properties Of Integro-delay Differential Equations," Communications in Nonlinear Science and Numerical Simulation, vol. 125, article no. 107320, Elsevier, Oct 2023.
The definitive version is available at https://doi.org/10.1016/j.cnsns.2023.107320
Mathematics and Statistics
Keywords and Phrases
Asymptotic stability (AS); Boundedness; Integrability; LKF; System of integro-delay differential equations; Uniform stability (US)
International Standard Serial Number (ISSN)
Article - Journal
© 2023 Elsevier, All rights reserved.
01 Oct 2023