On Oscillation of a Second Order Impulsive Linear Delay Differential Equation

For the delay differential equation m ¨x t. q ak t.x gk t..s0, gk t. Ft , ks1 with impulsive conditions x tj.sAjx t jy0.,˙x t j.sBj˙x t jy0., a connection between the following properties is established: nonoscillation of the differential equation and the corresponding differential inequality, positiveness of the fundamental function and the existence of a solution of a generalized Riccati inequality. Explicit conditions for nonoscillation and oscillation and comparison theorems are presented.