Oscillation of a second order impulsive linear delay differential equation

For the delay differential equation [GRAPHICS] with impulsive conditions x(tau(j)) = A(j)x(tau(j) - 0), (x) over dot(tau(j)) = B-j(x) over dot(tau(j) - 0), 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. (C) 1999 Academic Press.