An Exponential Estimate for Solutions of Linear Impulsive Delay Differential Equations

Abstract

This paper is concerned with linear impulsive delay differential equations with impulsive conditions allowing delays in the index of the jumps. We obtain an exponential estimate for the solutions of such types of equations. In preparation to this, we present three essential lemmas related to the adjoint equation, the representation of solutions and a bound for the fundamental matrix. Moreover, a sharper estimate is provided.