Oscillation and stability of first-order delay differential equations with retarded impulses

TL;DR

This paper investigates the oscillation and stability of first-order delay differential equations with retarded impulses, extending existing results by considering delays in both the continuous and impulsive parts.

Contribution

It introduces new criteria for oscillation and stability in impulsive differential equations with delays in both the continuous and impulse conditions.

Findings

Improved oscillation criteria for delayed impulsive differential equations.

Enhanced stability conditions considering retarded impulses.

Illustrative example demonstrating the theoretical results.

Abstract

In this paper, we study both the oscillation and the stability of impulsive differential equations when not only the continuous argument but also the impulse condition involves delay. The results obtained in the present paper improve and generalize the main results of the key references in this subject. An illustrative example is also provided.