Oscillation criteria of second-order half-linear dynamic equations on time scales

In this paper, by using the Riccati transformation technique, chain rule and inequality A(lambda) - lambdaAB(lambda-1) + (lambda - 1) B-lambda greater than or equal to, 0, lambda greater than or equal to 1, where A and B are positive constants, we will establish some oscillation criteria for the second-order half-linear dynamic equation (p(t) (x(Delta)(t))(gamma))(Delta) + q (t)x(gamma)(t) = 0, t is an element of [a, b] on time scales, where gamma > 1 is an odd positive integer. Our results not only unify the oscillation of half-linear differential and half-linear difference equations but can be applied on different types of time scales and improve some well-known results in the difference equation case. Some examples are considered here to illustrate our main results. (C) 2004 Published by Elsevier B.V.