The authors investigate oscillatory properties of the matrix Sturm-Liouville dynamic equation on a time scale (which is supposed to be unbounded from above)
where are symmetric -matrices and is positive definite. Basic facts of the time scale calculus can be found in the recent monograph of M. Bohner and A. Peterson [Dynamic equations on time scales. An introduction with applications. Basel: Birkhäuser (2001; Zbl 0978.39001)]. Recall that the time scale derivative reduces to the usual derivative if and to the forward difference if . The forward jump operator is defined by and the graininess by . One of the main results of the paper reads as follows:
Suppose that for every there exist such that , and
where stands for the greatest eigenvalue of the matrix indicated. Then (*) with is oscillatory.
The general oscillation criteria presented in the paper are illustrated by a number of examples and corollaries.