On the oscillation of functional differential equations

In this paper we present certain criteria for the oscillation of functional differential equations of the form\documentclass{article}\pagestyle{empty}\begin{document}$$ x^{\left(n \right)} \left(t \right) + p\left(t \right)x^{\left({n ‐ 1} \right)} \left(t \right) + \delta H\left({t,x\left({g\left(t \right)} \right)} \right) = 0 $$\end{document}where δ = ±1, p, g: [t 0 , ∞) → IR, H: [t 0 ,∞) × IR → IR are continuous, p(t) ≥ 0 for t ≥ t 0 and lim t → ∞ g(t) — ∞. We like to point out that condition of the form\documentclass{article}\pagestyle{empty}\begin{document}$$ \int_{t_0}^\infty {\exp \left\{{‐ \int_{t_0}^t {p\left(u \right)du}} \right\}} dt = \infty $$\end{document}will not be employed.