A necessary and sufficient condition for oscillation of the Sturm–Liouville dynamic equation on time scales

摘要

In this paper, we investigate oscillatory properties of the second order Sturm–Liouville dynamic equation on a time scale (∗)(r(t)xΔ)Δ+c(t)xσ=0.Using the so-called trigonometric transformation we establish a necessary and sufficient condition for oscillation of (∗). This condition is then used to derive an explicit oscillation criterion for this equation.