Oscillation theorems for second-order nonlinear neutral differential equations

Abstract

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 ) x β ( σ ( t ) ) = 0 , where 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.