Date: 28 Sep 2006

Monotone semi-flows which have a monotone first integral

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Abstract

We present a fairly general study for a class of semi-flows defined on an abstract space, which are monotonically increasing and possess a first integral, also increasing. Examples of that are systems of delay differential equations generated by compartmental models. Under reasonable restrictions, a complete description of the asymptotic behavior can be obtained in situations including almost-periodic dependence. We will not go into these details here. Rather the paper intends to enlighten the main aspects of the theory. Finally, a comparison with related literature is made.