Oscillation of second-order delay and neutral delay dynamic equations on time scales

ABSTRACT. In this paper, we consider the second-order linear delay dynamic equation x(t) + q(t)x((t)) = 0; on a time scale T. We will study the properties of the solutions and establish some sucient conditions for oscillations. In the special case when T = R and (t) = t, our results include some well-known results in the literature for dierential equations. When, T = Z, T = hZ, for h> 0 and T = Tn = ftn: n 2 N0g where tng is the set of the harmonic numbers dened by t0 = 0, tn