Abstract
Necessary and sufficient conditions are established for oscillation of second-order neutral impulsive differential equation , , where the coefficients ; , and .
Highlights
Oscillation theory is one of the directions which initiated the investigations of the qualitative properties of differential equations
Many remarkable results for the oscillatory properties of various classes of impulsive differential equations can be found in the literature 2, 9–11
The notion of characteristic system was first introduced by Bainov and Simeonov 2 ; it can be used in obtaining of various necessary and sufficient conditions for oscillation of constant coefficients linear impulsive differential equations of first order with one or several deviating arguments
Summary
Oscillation theory is one of the directions which initiated the investigations of the qualitative properties of differential equations. The notion of characteristic system was first introduced by Bainov and Simeonov 2 ; it can be used in obtaining of various necessary and sufficient conditions for oscillation of constant coefficients linear impulsive differential equations of first order with one or several deviating arguments. Due to some obstacles of theoretical and technical character in handling with constant coefficients linear impulsive differential equations of second or higher order, there are no results which studied the necessary and sufficient conditions in monograph 2. How to establish the necessary and sufficient conditions for second order constant coefficients linear impulsive differential equations corresponding to their characteristic systems? We study and solve this problem for a class of linear impulsive differential equations of second order with advanced argument. 1.1 reduces to y t py t − τ qy t − σ 0
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