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arXiv · 1202.3529

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

Changjing Zhuge·Xiaojuan Sun·Jinzhi Lei
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Abstract

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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Changjing Zhuge, Xiaojuan Sun, Jinzhi Lei. 2012-02-16. On positive solutions and the Omega limit set for a class of delay differential equations. https://doi.org/10.3934/dcdsb.2013.18.2487

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