Oscillation of a Linear Delay Impulsive Differential Equation

L. Berezansky; E. Braverman

Oscillation of a Linear Delay Impulsive Differential Equation

funct-an 2008-02-03 v1 Dynamical Systems Functional Analysis

Authors: L. Berezansky , E. Braverman

Abstract

The main result of the paper is that the oscillation (non-oscillation) of the impulsive delay differential equation $\dot {x}(t)+\sum_{k=1}^m A_k(t)x[h_k(t)]=0,~~t\geq 0$ , $x(\tau_j)=B_jx(\tau_j-0), \lim \tau_j = \infty$ 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.

Cite

@article{arxiv.funct-an/9502002,
  title  = {Oscillation of a Linear Delay Impulsive Differential Equation},
  author = {L. Berezansky and E. Braverman},
  journal= {arXiv preprint arXiv:funct-an/9502002},
  year   = {2008}
}