Oscillation criteria for sublinear half-linear delay dynamic equations on time scales

This paper is concerned with oscillation of the second-order half-linear delay dynamic equation (r(t)(x∆)γ) ∆ + p(t)xγ(τ(t)) = 0, on a time scale T where 0 < γ ≤ 1 is the quotient of odd positive integers, p: T → [0,∞), and τ: T → T are positive rd-continuous functions, r(t) is a positive and (delta) differentiable function, τ(t) ≤ t, and lim t→ ∞ τ(t) = ∞. We es-tablish some new sufficient conditions which ensure that every solution oscillates or converges to zero. Our results in the special cases when T = R and T = N involve and improve some oscillation results for second-order differential and dif-ference equations; and when T = hN, T = qN0 and T = N2 our oscillation results are essentially new. Some examples illustrating the importance of our results are also included