Bulletin of the
Korean Mathematical Society BKMS

By means of a Riccati transform and averaging technique some oscillation criteria are established for perturbed nonlinear differential equations of second order $$ (p(t)x'(t))'+q(t)|x(\phi(t))|^{\alpha+1} \text{sgn}\,x(\phi(t)) + g(t,x(t))=0 \tag{$P_1$} $$ ($P_2$) and ($P_3$) satisfying the condition (H). A comparison theorem and examples are given.

Keywords: Riccati transform, oscillatory property, delay differential equation, comparison theorem

MSC numbers: 34C10, 34C15