Linearized oscillations for even-order neutral differential equations (Q805858)

For the n-th order neutral delay differential equation of the form \[ (d^ n/dt^ n)[y(t)-P(t)G(y(t-\tau))+Q(t)H(y(t-\sigma))]=0, \] where P, Q are positive functions, a comparison theorem is given under certain conditions. Conditions are given implying the oscillation of the bounded solutions of the nonlinear equation in case of the oscillation of all bounded solutions of the linearized equation. It is also proved that such equations may have nonoscillatory solutions.