Employing notions and calculus developed in [B. Aulbach
and S. Hilger
, Nonlinear dynamics and quantum dynamical systems, Contrib. Int. Semin., ISAM-90, Gaussig/GDR 1990, Math. Res. 59, 9-20 (1990; Zbl 0719.34088
)] and results from a preceding own paper [Existence and comparison results for dynamic systems on time scales. J. Math. Anal. Appl. (to appear)], the author extends the method of upper and lower solutions to dynamical systems on time scales,
. He uses monotone iterative technique for initial value problems and periodic boundary value problems in order to obtain extremal solutions.