BASIC CONCEPTS OF FUNCTIONAL-DIFFERENTIAL EQUATIONS AND THEOREMS ON THE STABILITY OF THEIR SOLUTIONS (INTERNATIONAL JOURNAL OF SCIENCE AND TECHNOLOGY, 2025)
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.