QUALITATIVE ANALYSIS of INTEGRO-DIFFERENTIAL EQUATIONS with VARIABLE RETARDATION
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.
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
Mathematics and Statistics
Keywords and Phrases
Boundedness at infinity; Integrability; Lyapunov–Krasovskiĭ functional; Stability; Volterra RIDEs
International Standard Serial Number (ISSN)
Article - Journal
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01 Feb 2022