Oscillation of second-order nonlinear neutral dynamic equations on time scales with distributed deviating arguments

Abstract

This article is concerned with oscillation of second-order neutral dynamic equations with distributed deviating arguments of the form ( r ( t ) ( ( y ( t ) + p ( t ) y ( τ ( t ) ) ) Δ ) γ ) Δ + ∫ c d f ( t , y ( θ ( t , ξ ) ) ) Δ ξ = 0 , where γ > 0 is a ratio of odd positive integers with r ( t ) and p ( t ) real-valued rd-continuous positive functions defined on T . We establish some new oscillation criteria and give sufficient conditions to insure that all solutions of nonlinear neutral dynamic equation are oscillatory on a time scale T .