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Zbl 1050.34098
Yan, Jurang
Oscillation properties of a second-order impulsive delay differential equation.
(English)
[J] Comput. Math. Appl. 47, No. 2-3, 253-258 (2004). ISSN 0898-1221

Summary: For the second-order delay differential equation $$y''(t)+ a(t)y'(t)+ \sum^n_{i=1} p_i(t) y\bigl(g_i(t)\bigr)=0,\quad t>0,\ t\in t_k,$$ with the impulsive conditions $$y(t^+_k)-y(t_k^-)= b_ky(t_k^-),\quad y'(t^+_k)-y'(t_k^-)= b_ky' (t_k^-),$$ an explicit necessary and sufficient condition for all bounded solutions to be oscillatory is obtained by the comparison theorem on bounded oscillation of the impulsive differential equation with the corresponding nonimpulsive differential equation.
MSC 2000:
*34K11 Oscillation theory of functional-differential equations
34K45 Equations with impulses

Keywords: Impulsive delay equation; Oscillation; Nonoscillation

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