On positive solutions and the Omega limit set for a class of delay differential equations

Details On positive solutions and the Omega limit set for a class of delay differential equations On positive solutions and the Omega limit set for a class of delay differential equations

2012-02-16

arxiv.org/abs/1202.3529v1

Mathematics

Classical Analysis and ODEs

15 pages, 2 figures

Scientific paper

This paper studies the positive solutions of a class of delay differential equations with two delays. These equations originate from the modeling of hematopoietic cell populations. We give a sufficient condition on the initial function for $t\leq 0$ such that the solution is positive for all time $t>0$. The condition is "optimal". We also discuss the long time behavior of these positive solutions through a dynamical system on the space of continuous functions. We give a characteristic description of the $\omega$ limit set of this dynamical system, which can provide informations about the long time behavior of positive solutions of the delay differential equation.

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