Vol. 2 No. 13 (2025): International Journal Science and Technology
Articles

BASIC CONCEPTS OF FUNCTIONAL-DIFFERENTIAL EQUATIONS AND THEOREMS ON THE STABILITY OF THEIR SOLUTIONS

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  • A. Akhmatov Azizbek,
  • Kh. Khusanov Djumma

Published 18-10-2025

Keywords

  • Functional-differential equations, stability, Lyapunov functional, limiting equation, asymptotic stability, metric, precompactness, space of continuous functions.
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

BASIC CONCEPTS OF FUNCTIONAL-DIFFERENTIAL EQUATIONS AND THEOREMS ON THE STABILITY OF THEIR SOLUTIONS. (2025). INTERNATIONAL JOURNAL OF SCIENCE AND TECHNOLOGY, 2(13), 26-30. https://doi.org/10.70728/tech.v02.i13.006

Abstract

This article examines functional-differential equations with delay and investigates the stability properties of their solutions. The main focus is placed on the characteristics of solutions in metric spaces of functions, the application of Lyapunov functionals for stability analysis, and the precompactness of shift families. The asymptotic behavior of solutions is studied through the concepts of limiting functions and limiting equations. Theorems on uniform asymptotic stability based on Lyapunov functionals are presented.

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