Stability in the class of first order delay differential equations

TL;DR

This paper investigates the stability of first order delay differential equations, focusing on whether approximate solutions remain close to true solutions, thereby addressing the robustness of solutions under perturbations.

Contribution

It provides a new analysis of stability in delay differential equations, establishing conditions under which approximate solutions are close to exact solutions.

Findings

Approximate solutions stay close to true solutions under certain conditions.

The stability criteria are explicitly characterized for first order delay differential equations.

Results enhance understanding of solution robustness in delay differential equations.

Abstract

The main aim of this paper is the investigation of the stability problem for ordinary delay differential equations. More precisely, we would like to study the following problem. Assume that for a continuous function a given delay differential equation is fulfilled only approximately. Is it true that in this case this function is close to an exact solution of this delay differential equation?