Oscillation theorems for higher order neutral differential equations

The aim of this paper is to study the asymptotic properties and oscillation of the nth order neutral differential equationsequation(E)(r(t)[x(t)+p(t)x(τ(t))](n-1))′+q(t)x(σ(t))=0.r(t)x(t)+p(t)x(τ(t))(n-1)′+q(t)x(σ(t))=0.Obtained results are based on the new comparison theorems, that permit to reduce the problem of the oscillation of the nth order equation to the oscillation of a set of the first order equation. Obtained comparison principles essentially simplify the examination of studied equations and allow to relax some conditions imposed on the coefficients of (E).