Monotonicity with respect to closed convex cones II

Abstract

Consider the flow ψt for the system of differential equations open. Let K(t) be a closed convex expanding cone whenever and the smallest subspace containing K(t) for each t is the same for all t)k be a unit vector in K(0), and . If for some positive l leaves K(t) invariant for all t then for all . If in addition takes k into the relative interior of K(t) for all t then is in the relative interior of K(t) for all t > 0. These and related results are extensions of the Kamke—Möller theorem and Hirsch's theorem for strong monotone flows. Applications from chemical kinetics and epidemiology are given.