Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 07, pp. 1-18.

Title: Existence and stabilization for impulsive differential equations of
second order with multiple delays
       
Authors: Sandra Pinelas (Academia Militar, Amadora, Portugal)
         Osman Tunc (Van Yuzuncu Yil Univ.  Van , Turkey)
         Erdal Korkmaz (Mus Alparslan Univ., Mus, Turkey)
         Cemil Tunc (Van Yuzuncu Yil Univ.  Van , Turkey)

Abstract: 
Existence and stability of solutions are important parts in the qualitative study
of delay differential equations. The stabilizing by imposing proper
impulse controls are used in many areas of natural sciences and engineering.
This article provides sufficient conditions for the existence and exponential
stabilization of solutions to delay impulsive differential equations
of second-order with multiple delays.
The main tools in this article are the Schaefer fixed point theorem,
fixed impulse effects, and Lyapunov-Krasovskii functionals.
The outcomes extend earlier results in the literature.

Submitted August 23, 2023. Published January 23, 2024.
Math Subject Classifications: 34A37, 34K45.
Key Words: Impulsive delay differential equations, exponentially stabilization, existence of solutions;  multiple delays.