Existence and Stabilization for Impulsive Integro-Differential Equations of Second-Order with Multiple Kernels and Delays

Abstract

The mathematical formulation of many dynamic systems naturally culminates in the second-order impulsive delay integro-differential equations (IPDIDEs). This study focuses on existence and stabilization results for the second-order IPDIDEs containing multiple time delays. Initially, the existence of a solution is established using Schaefer's fixed point theorem. Following this, the stabilization result is derived through the method of Lyapunov-Krasovskii functionals. The findings of this study improve upon and extend several well-known results in the existing literature. In a specific case, we present an example that demonstrates the applicability of our results.