Oscillations of Second Order Impulsive Differential Equations with Advanced Arguments

Abstract

A comparison theorem providing sufficient conditions for the oscillation of all solutions of a class of second order linear impulsive differential equations with advanced argument is formulated. A relation between the oscillation (non-oscillation) of second order impulsive differential equations with advanced arguments and the oscillation (nonoscillation) of the corresponding impulsive ordinary differential equations is established by means of the Lebesgue dominated convergence theorem. Obtained comparison principle essentially simplifies the examination of the studied equations.