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 $\dot{x}(t)+{\sum }_{k=1}^m{A}_k(t)x[h_k(t)]=0,t\ge 0$, $x({\tau }_j)=B_{j}x({\tau }_j-0),\lim {\tau }_j=\infty$ is equivalent to the oscillation (non-oscillation) of the equation without impulses $\dot{x}(t)={\sum }_{k=1}^m{A}_k(t){\prod }_{h_k(t)<{\tau }_j\le t}{B}_j^{-1}x[h_k(t)]=0,t\ge 0$. Explicit oscillation results are presented.

17 pages, latex, no figures

Cited by in corpus (1)

• Oscillation and nonoscillation criteria for impulsive delay differential equations with Perron integrable righthand sides