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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

Citations:

Zbl 0719.34088
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