Asymptotic properties of solutions to linear nonautonomous delay differential equations through generalized characteristic equations

TL;DR

This paper investigates the long-term behavior of solutions to nonautonomous delay differential equations by analyzing their associated generalized characteristic equations.

Contribution

It introduces new methods to understand the asymptotic properties of solutions based on the solutions of generalized characteristic equations.

Findings

Characterization of asymptotic behavior of solutions

Conditions for stability and decay rates

Extension of classical results to nonautonomous cases

Abstract

We study some properties concerning the asymptotic behavior of solutions to nonautonomous retarded functional differential equations, depending on the knowledge of certain solutions of the associated generalized characteristic equation.