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Zbl 0783.34005
Kaymakçalan, Billur
Monotone iterative method for dynamic systems on time scales.
(English)
[J] Dyn. Syst. Appl. 2, No.2, 213-220 (1993). ISSN 1056-2176

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.
[W.Müller (Berlin)]
MSC 2000:
*34A45 Theoretical approximation of solutions of ODE
37-99 Dynamic systems and ergodic theory
34C11 Qualitative theory of solutions of ODE: Growth, etc.
34A34 Nonlinear ODE and systems, general
34C25 Periodic solutions of ODE

Keywords: method of upper and lower solutions; dynamical systems on time scales; monotone iterative technique; initial value problems; periodic boundary value problems; extremal solutions

Citations: Zbl 0719.34088

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