Oscillation theorems for second-order nonlinear neutral differential equations

The purpose of this paper is to study the oscillation of the second-order neutral differential equations of the form (a(t)[z′(t)]γ)′+q(t)xβ(σ(t))=0,(a(t)[z′(t)]γ)′+q(t)xβ(σ(t))=0, where z(t)=x(t)+p(t)x(τ(t))z(t)=x(t)+p(t)x(τ(t)). We explore properties of given equations by examining those of associated first-order delay equations. New comparison theorems essentially simplify the examination of the equations studied as they allow us to deduce the oscillation of the second-order delay differential equation by applying the oscillation criteria obtained to the first-order delay equations. The results obtained are easy to verify.