Hille and Nehari type criteria for third-order dynamic equations

In this paper, we extend the oscillation criteria that have been established by Hille [E. Hille, Nonoscillation theorems, Trans. Amer. Math. Soc. 64 (1948) 234–252] and Nehari [Z. Nehari, Oscillation criteria for second-order linear differential equations, Trans. Amer. Math. Soc. 85 (1957) 428–445] for second-order differential equations to third-order dynamic equations on an arbitrary time scale T, which is unbounded above. Our results are essentially new even for third-order differential and difference equations, i.e., when T = R and T = N. We consider several examples to illustrate our results. © 2006 Elsevier Inc. All rights reserved