*(English)*Zbl 1056.34050

This paper is concerned with oscillation theory for selfadjoint second-order scalar dynamic equations of the form

on time scales $\mathbb{T}$. Here, a time scale is an arbitrary nonempty closed subset of the real numbers, denoted as measure chain by the authors, ${x}^{{\Delta}}$ stands for the ${\Delta}$-derivative of $x$ and ${x}^{\sigma}$ is the composition of $x$ with the forward jump operator $\sigma $. Furthermore, $p,q:\mathbb{T}\to \mathbb{R}$ are assumed to be rd-continuous.

The authors provide Kamenev-type and interval oscillation criteria for such linear dynamic equations on time scales. These criteria generalize corresponding theorems for ODEs by *Ch. G. Philos* [Arch. Math. 53, 482–492 (1989; Zbl 0661.34030)] or the second author [J. Math. Anal. Appl. 229, 258–270 (1999; Zbl 0924.34026)], respectively, and are new for difference equations in particular. The paper closes with four examples illustrating the obtained results, two of them for difference equations and one on a time scale with unbounded graininess.