Existence of Nonoscillatory Solutions of First Order Neutral Delay Dynamic Equation on Time Scales

In this paper,we will establish some sufficient conditions for the existence of nonoscillatory solutions of the first order delay dynamic equation (x(t) + cx(t τ))^Δ +p(t)x(t - γ) = 0 on a time scale T, where c ∈ ℝ, τ, γ ≥ 0, σ = max{τ, γ}, p(t) is a rd-continuous function defined on T. Our results as a special case when T = ℝ and T = ℕ, involve and improve some nonoscillation results.