New oscillation criteria for the second order nonlinear neutral delay differential equation [y(t) + p(t)y(t− τ)]′′ + q(t) f(y(g(t))) = 0, t ≥ t0 are given. The relevance of our theorems becomes clear due to a carefully selected example.

In this paper, a higher order nonlinear neutral functional differential equation with distributed delay is studied by using the continuation theorem of coincidence degree theory. Some new results on the existence of periodic solutions are obtained. Keywords—Neutral functional differential equation, higher order, periodic solution, coincidence degree theory