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 [r(t)Φ(x^Δ)]^Δ + c(t)Φ(x^σ) = 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) ≠ 0 (instead r(t) > 0).