## Monotone iterative method for dynamic systems on time scales.(English)Zbl 0783.34005

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, $$u^ \Delta= f(t,u)$$, $$u(0)=u_ 0$$, $$f\in C_{rd} [T^ k\times \mathbb{R}, \mathbb{R}]$$. He uses monotone iterative technique for initial value problems and periodic boundary value problems in order to obtain extremal solutions.
Reviewer: W.Müller (Berlin)

### MSC:

 34A45 Theoretical approximation of solutions to ordinary differential equations 37-XX Dynamical systems and ergodic theory 34C11 Growth and boundedness of solutions to ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 34C25 Periodic solutions to ordinary differential equations

Zbl 0719.34088