Oscillation criteria for third-order neutral dynamic equations with continuously distributed delay

It is the purpose of this paper to give oscillation criteria for the third-order neutral dynamic equations with continuously distributed delay, [r(t)([x(t) + integral(b)(a) p(t,eta)x[tau(t,eta)]Delta eta](Delta Delta))(gamma)](Delta) + integral(d)(c) q(t,xi)f(x[phi(t,xi)])Delta xi = 0, on a time scale T, where gamma is the quotient of odd positive integers. By using a generalized Riccati transformation and an integral averaging technique, we establish some new sufficient conditions which ensure that every solution of this equation oscillates or converges to zero.