A telescoping principle for oscillation of the second order half-linear dynamic equations on time scales

We establish the so-called ``telescoping principle" for oscillation of the second order half-linear dynamic equation $$\Bl[r(t)\Phi\bl(x^{\Delta }\br)\Br]^\Delta + c(t)\Phi(x^\sigma)=0$$ on a time scale. This principle provides a method enabling us to construct many new oscillatory equations. Unlike previous works concerning the telescoping principle, we formulate some oscillation results under the weaker assumption $r(t)\not=0$ (instead $r(t)>0$).