Oscillation of a Linear Delay Impulsive Differential Equation

Abstract

The main result of the paper is that the oscillation (non-oscillation) of the impulsive delay differential equation $\dot {x}(t)+\sum_{k=1}^m A_k(t)x[h_k(t)]=0,~~t\geq 0$, $x(τ_j)=B_jx(τ_j-0), \lim τ_j = \infty$ is equivalent to the oscillation (non-oscillation) of the equation without impulses $\dot {x}(t)=\sum_{k=1}^m A_k(t) \prod_{h_k(t)<τ_j\leq t} B_j^{-1}x[h_k(t)]=0, t \geq 0$. Explicit oscillation results are presented.