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.