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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.
AMS:
1Research of this author supported by a Natural Sciences and Engineering Research Council of Canada Indiv~dual Research Grant.
1Research of this author supported by a Natural Sciences and Engineering Research Council of Canada Indiv~dual Research Grant.
Notes
1Research of this author supported by a Natural Sciences and Engineering Research Council of Canada Indiv~dual Research Grant.