Nonlinear oscillation of second‐order neutral dynamic equations with distributed delay

In this paper, we consider the nonlinear oscillation of the following second‐order neutral delay dynamic equations with distributed delayr ( t ) | Z Δ ( t ) | α − 1Z Δ ( t )Δ + ∫ c d q ( t , ξ ) | x ( θ ( t , ξ ) ) | β − 1 x ( θ ( t , ξ ) ) Δξ = 0on a time scale T , where Z ( t ) = x ( t ) + p ( t ) x ( τ ( t )), α , β > 0 are constants. By using some new techniques, we obtain oscillation criteria for the equation when β > α , β = α , and β < α , respectively. Those results established here complete and develop the oscillation criteria in the literature. Also, our main results are illustrated with some examples. Copyright © 2015 John Wiley & Sons, Ltd.