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Oscillation and nonoscillation for second order linear impulsive differential equations. (English) Zbl 0895.34031
The author establishes an oscillation theorem for linear impulsive differential equations (*) u '' =-p(t)u, t0, where p(t) is an impulsive function defined by p(t)= n=1 a n δ(t-t n ) with a n >0 for all n and 0t 0 <t 1 <t 2 <<t n <, t n as n. 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 +λ n-1 T, λ>1, T>0, and t n =t 0 +nT.

MSC:
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34A37Differential equations with impulses