QUALITATIVE ANALYSIS of INTEGRO-DIFFERENTIAL EQUATIONS with VARIABLE RETARDATION

Author

Martin Bohner, Missouri University of Science and TechnologyFollow
Osman Tunç

Abstract

The paper is concerned with a class of nonlinear time-varying retarded integro-differential equations (RIDEs). By the Lyapunov–Krasovskiĭ functional method, two new results with weaker conditions related to uniform stability (US), uniform asymptotic stability (UAS), integrability, boundedness, and boundedness at infinity of solutions of the RIDEs are given. For illustrative purposes, two examples are provided. The study of the results of this paper shows that the given theorems are not only applicable to time-varying linear RIDEs, but also applicable to time-varying nonlinear RIDEs.

Recommended Citation

M. Bohner and O. Tunç, "QUALITATIVE ANALYSIS of INTEGRO-DIFFERENTIAL EQUATIONS with VARIABLE RETARDATION," Discrete and Continuous Dynamical Systems - Series B, vol. 27, no. 2, pp. 639 - 657, American Institute of Mathematical Sciences (AIMS), Feb 2022.

The definitive version is available at https://doi.org/10.3934/DCDSB.2021059

Department(s)

Mathematics and Statistics

Keywords and Phrases

Boundedness at infinity; Integrability; Lyapunov–Krasovskiĭ functional; Stability; Volterra RIDEs

International Standard Serial Number (ISSN)

1531-3492

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 American Institute of Mathematical Sciences (AIMS), All rights reserved.

Publication Date

01 Feb 2022