Some Oscillation Problems for a Second Order Linear Delay Differential Equation

For the delay differential equation m ¨x t.q ak t.x gk t..s0, gk t.Ft, ks1 a connection between the following properties is established: non-oscillation of the differential equation and the corresponding differential inequality, positiveness of the fundamental function, and the existence of a nonnegative solution of a generalized Riccati inequality. Explicit conditions for non-oscillation and oscillation and comparison theorems are presented.