Oscillation of a Linear Delay Impulsive Differential Equation

Details Oscillation of a Linear Delay Impulsive Differential Equation Oscillation of a Linear Delay Impulsive Differential Equation

1995-02-07

arxiv.org/abs/funct-an/9502002v1

Mathematics

Dynamical Systems

17 pages, latex, no figures

Scientific paper

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

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