Oscillation criteria for certain third-order delay dynamic equations

This paper is concerned with the oscillatory behavior of a certain class of third-order nonlinear variable delay neutral functional dynamic equations, {r(t)phi([a(t)y(Delta)(t)](Delta))}(Delta) + P(t)F(phi(x(delta(t)))) = 0, on a time scale T with supT = +infinity, where y(t) = x(t) + B(t)g(x(tau(t))), phi(u) = vertical bar u vertical bar(lambda-1)u, lambda >= 1. By using the generalized Riccati transformation and a lot of inequality techniques, some new oscillation criteria for the equations are established, results are presented that not only complement and improve those related results in the literature, but also improve some known results for a third-order delay dynamic equation with a neutral term. Further, the main results improve some related results for third-order neutral differential equations. Some examples are given to illustrate the importance of our results.