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

Abstract

In this paper, we establish the so-called ``\textit{telescoping principle}" for oscillation of the second order half-linear dynamic equation $$[r(t)\Phi(x^{\Delta })]^\Delta + c(t)\Phi(x^{\sigma})=0$$ 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 $r(t)>0$).