多地区多向流动的人口发展系统

在1]中宋健等提出了 n 个地区的人口发展系统的数学模型之后,对 n=1 的情况已经有了很好的结论.这些结论对人口数量变化趋势的说明以及对我国的计划生育工作能起一定的参考作用.本文就 n 个地区多向流动的人口发展系统进行讨论,这个问题在1]中归结为如下的积微分方程组,数学上习惯称之为第四类方程.

AN n-DISTRICT MIGRATING POPULATION DEVELOPING SYSTEM

Since Song Jian et al.gave the n-district population developing equations in 1],many re-sults have been obtained for n=1,but only few papers discussed the case n>1.In this paper atheorem on uniquencess and the existence of n-district population equations is proved and thespectral properties of the n-district population operator A+B are discussed,and a necessary andsufficient condition of the stability is given.