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Zbl 0895.34031
Huang, Chunchao
Oscillation and nonoscillation for second order linear impulsive differential equations.
(English)
[J] J. Math. Anal. Appl. 214, No.2, 378-394 (1997). ISSN 0022-247X

The author establishes an oscillation theorem for linear impulsive differential equations (*) $u''=-p(t)u$, $t\ge 0$, 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 $n\in \bbfN$ and $0\le t_0<t_1 <t_2< \cdots <t_n<\dots$, $t_n\to\infty$ 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 $t_n= t_0+nT$.
[N.Hayek (La Laguna)]
MSC 2000:
*34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
34A37 Differential equations with impulses

Keywords: linear impulsive differential equations; nonoscillation; oscillation

Cited in: Zbl 1140.34304

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