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Oscillation properties of a second-order impulsive delay differential equation. (English) Zbl 1050.34098

Summary: For the second-order delay differential equation

y '' (t)+a(t)y ' (t)+ i=1 n p i (t)yg i (t)=0,t>0,tt k ,

with the impulsive conditions

y(t k + )-y(t k - )=b k y(t k - ),y ' (t k + )-y ' (t k - )=b k y ' (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:
34K11Oscillation theory of functional-differential equations
34K45Functional-differential equations with impulses