Abstract :
This paper is concerned with oscillation of the second-order half-linear dynamic equation
r(t) x γ + p(t)xγ (t) = 0,
on a time scale T where γ is the quotient of odd positive integers, r(t) and p(t) are
positive rd-continuous functions on T. Our results solve a problem posed by [R.P. Agarwal,
D. O’Regan, S.H. Saker, Philos-type oscillation criteria for second-order half linear dynamic
equations, Rocky Mountain J. Math. 37 (2007) 1085–1104; S.H. Saker, Oscillation criteria
of second order half-linear dynamic equations on time scales, J. Comput. Appl. Math. 177
(2005) 375–387] and our results in the special cases when T = R and T = Z involve and
improve some oscillation results for second-order differential and difference equations; and
when T = hZ, T = qN0 and T = N20
, etc., our oscillation results are essentially new. Some
examples illustrating the importance of our results are also included
