Summary: We establish a new interval oscillation criterion for the second-order half-linear dynamic equation
on a time scale which is unbounded. This criterion is an extension of the oscillation result for second order linear dynamic equation established by L. Erbe, A. Peterson and S. H. Saker [J. Difference Equ. Appl. 14, No. 10–11, 997–1009 (2008; Zbl 1168.34025)]. As an application, we obtain a sufficient condition for oscillation of the second-order half-linear differential equation
where , are odd positive integers.