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Monotone iterative method for dynamic systems on time scales. (English) Zbl 0783.34005
Employing notions and calculus developed in [{\it B. Aulbach} and {\it 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, $u\sp \Delta= f(t,u)$, $u(0)=u\sb 0$, $f\in C\sb{rd} [T\sp k\times \bbfR, \bbfR]$. He uses monotone iterative technique for initial value problems and periodic boundary value problems in order to obtain extremal solutions.

34A45Theoretical approximation of solutions of ODE
37-99Dynamic systems and ergodic theory (MSC2000)
34C11Qualitative theory of solutions of ODE: growth, boundedness
34A34Nonlinear ODE and systems, general
34C25Periodic solutions of ODE