Some oscillation results for second order functional dynamic equations¹

In this paper, we consider the second-order nonlinear dynamic equation on a time scale 핋. Our goal is to establish some new oscillation and non-oscillation results for this equation. Here we assume that τ (t) ≤ t ≤ ξ (t) and τ, ξ: 핋 → 핋, and use the notation x^τ (t) = x (τ (t)), x^σ (t) = x (σ (t)) and x^ξ (t) = x (ξ (t)). We apply results from the theory of lower and upper solutions for related dynamic equations along with some additional estimates on the positive solutions.