数学物理学报(英文版) ›› 1982, Vol. 2 ›› Issue (2): 139-148.
宋健1, 于景元1, 王彦祖1, 胡顺菊2, 赵忠信3, 刘嘉荃3, 冯德兴3, 朱广田3
Song jian1, Yu Jing yuan1, Wang Xian zu1, Hu Shun ju2, Zhao Zhong xin3, Liu Jia quan3, Feng De xing3, Zhu Guang tian3
摘要: In this paper we discuss the spectral properties of the Population operator, prove that the population operator has only one real eigenvalue γ0, which is greater that real parts of other eigenvalues,and find the corresponding relation between γ0 and the critical fertility rate βcr. We also study the existence and asymptotic behaviour of the semigroup for the population system, then come to the conclusion about the stability of the population system,including the existene of the steaby population state in the critical case of the fertility rate.These are all the new results of the quantitative population theory.