Oscillation Criteria for Second Order Linear Differential Equations

Some oscillation criteria are given for the second order linear differential equation [r(t)u′(t)]′ + c(t)u(t) = 0, where r(t) ∈ C1([t0, ∞); (0, ∞)) and c(t) ∈ C([t0, ∞); R). These results improve oscillation criteria of Wintner, Hartman, Kamenev, Yan, and Philos by using a generalized Riccati transformation ν(t) = a(t)r(t){u′(t)/u(t) + f(t)}, where f ∈ C1 is a given function on [t0, ∞) and a(t) = exp{−2 ∫tf(s) ds}.