Monotone flows and fixed points for dynamic systems on time scales. (English) Zbl 0808.58036
The paper treats dynamic systems on time scales (closed subsets of reals) which include the discrete and continuous dynamic systems. It is first proved a basic result relative to a system of dynamic inequalities. Then one applies it to study monotone flows and stationary points.
Reviewer: D.Motreanu (Iaşi)
References:
| [1] | Aulbach, B.; Hilger, S., Linear dynamics processes with inhomogeneous time scales, (Nonlinear Dynamics and Quantum Dynamical Systems (1990), Akademie-Verlag: Akademie-Verlag Berlin), 9-20 · Zbl 0719.34088 |
| [2] | Aulbach, B.; Hilger, S., A unified approach to continuous and discrete dynamics, (Differential Equations: Qualitative Theory. Differential Equations: Qualitative Theory, Colloq. Math. Soc. Janos Bolya (1988), North-Holland), 37-56 · Zbl 0713.34050 |
| [3] | Kaymakçalan, B., Existence and comparison results for dynamic systems on a time scale, JMAA, 172, 243-255 (1993) · Zbl 0791.34007 |
| [4] | Kaymakçalan, B., Lyapunov stability theory for dynamic systems on time scales, JAMSA, 15, 275-281 (1992) · Zbl 0762.34027 |
| [5] | B. Kaymakçalan, Linear and nonlinear variation of parameters formula for dynamic systems on time scales, (to appear).; B. Kaymakçalan, Linear and nonlinear variation of parameters formula for dynamic systems on time scales, (to appear). |
| [6] | B. Kaymakçalan, Monotone iterative method for dynamic systems on time scales, Dynamic Systems and Appl.; B. Kaymakçalan, Monotone iterative method for dynamic systems on time scales, Dynamic Systems and Appl. |
| [7] | J.L. Gouze and K.P. Hadeler, Monotone flows and ordered intervals, Nonlinear World; J.L. Gouze and K.P. Hadeler, Monotone flows and ordered intervals, Nonlinear World · Zbl 0803.65076 |
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