Oscillation behavior of \(n\)th order neutral differential equations with continuous delay. (Q1426984)

The authors study the \(n\)th-order nonlinear neutral differential equation \[ \left[x(t)+\int_a^bp(t,\mu)x(\tau,\mu)d\mu\right]^{(n)}+ \lambda\int_c^dq(t,\xi)f(x(\sigma,\xi))d\xi=h(t). \] They establish sufficient conditions which ensure that all solutions are either oscillatory or satisfy \(\lim_{t\to\infty}| x(t)| =\infty\) or else \(\liminf_{t\to\infty}| x(t)| =0\). Some examples show the applicability of the results of this paper.