Oscillation and nonoscillation for second order linear impulsive differential equations (Q1380357)

The author establishes an oscillation theorem for linear impulsive differential equations (*) \(u''=-p(t)u\), \(t\geq 0\), where \(p(t)\) is an impulsive function defined by \(p(t)= \sum^\infty_{n=1} a_n \delta (t-t_n)\) with \(a_n>0\) for all \(n\in \mathbb{N}\) and \(0\leq t_0<t_1 <t_2< \cdots <t_n<\dots\), \(t_n\to\infty\) as \(n\to\infty\). Next, this result is applied to derive sufficient conditions for the nonoscillation and oscillation of (*) in each one of the particular cases corresponding to \(t_n=t_0+ \lambda^{n-1}T\), \(\lambda>1\), \(T>0\), and \(t_n= t_0+nT\).