Qualitative properties of solutions of second-order linear ODE with impulses

This paper studies the oscillation and nonoscillation of solutions of second-order linear ordinary differential equations with impulses. Our results show that the oscillatory behavior of all solutions of differential equations without impulses can be inherited by impulsive differential equations under certain impulsive perturbations. It is also seen that the oscillatory properties of all solutions of impulsive differential equations may be caused by the impulsive perturbations though the corresponding differential equations without impulses admits a nonoscillatory solution.