A graph theoretical approach to monotonicity with respect to initial conditions. (English) Zbl 0808.34003
Liu, Xinzhi (ed.) et al., Comparison methods and stability theory. The Symposium was held in Waterloo, Ontario, Canada, June 3-6, 1993. Proceedings. Basel: Marcel Dekker. Lect. Notes Pure Appl. Math. 162, 207-216 (1994).
From the Introduction: “Mathematical conditions for monotone and order preserving flows with respect to an orthant are well known. However, conditions for a single component of a system of ordinary differential equations to be monotone with respect to changes in a single initial value of some component in the system have not been developed. We present a graph theoretical approach to this question. An equivalent graphical condition for a flow to be order preserving with respect to an orthant will be given. Sufficient graphical conditions will be given for more general monotonicity results, including a result guaranteeing strictly positive or negative derivations of components with respect to initial conditions”.
For the entire collection see [Zbl 0798.00012].
For the entire collection see [Zbl 0798.00012].
Reviewer: A.Kachurovskij (Novosibirsk)
MSC:
| 34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
| 34C11 | Growth and boundedness of solutions to ordinary differential equations |
