Oscillation behavior of even order neutral differential equations with variable coefficients (Q1031716)

The following comparison theorem is the main result in this paper. Theorem. Assume that there exists a constant \(0<\lambda_0<1\) such that the first-order delay differential equation \[ z'+\frac{\lambda_0}{(n-1)!}\;q(t)\sigma^{(n-1}(t)[1-p(\sigma(t)]z(\sigma(t))=0 \] is oscillatory; then \[ [x(t)+p(t)x(\tau(t))]^{(n)}+q(t)x(\sigma(t))=0,(n:\text{even}) \] is oscillatory for even \(n\).