Development of approaches to the Myshkis problem on the stability of a first-order differential equation with aftereffect
0000-0002-7574-793X The material was received by the Editorial Board: 31.08.2025
We obtain sufficient stability conditions for a scalar linear nonautonomous first-order delay differential equation. The conditions are explicitly expressed in terms of parameters of the given equation, and strengthen existing results derived from the classical Myshkis theorems on $3/2$. We provide a detailed comparison of the new stability conditions with existing ones. The new approach yields significantly improved results when applied to equations with a single concentrated delay, and can be extended to broader classes of equations.
УДК 517.929
Keywords: differential equation, aftereffect, stability, Cauchy function, 3/2 Theorem.
________References: Kirill M. Chudinov Development of approaches to the Myshkis problem on the stability of a first-order differential equation with aftereffect. Mat. Trudy. 2026, 29, № 1. P. 142–162. DOI: 10.25205/1560-750X-2026-29-1-142-162