具年龄结构的周期种群系统的最优生育率控制

Optimal fertility rate control for a linear periodic age-dependent population system

讨论一类具有年龄结构的周期种群系统的最优生育率控制问题.运用偏微分方程的特征线理论和泛函分析方法,证明了该种群系统解的存在性及解对控制变量的连续相依性.利用Mazur's定理证明了最优生育率控制的存在性.

This paper discussed a linear periodic problem of the optimal fertility rate control for a class of agedependent population system. The existence of the solution and the continuous dependence of the solution on the control variable was proved by the characteristic line theory in differential equations and functional analysis method. The existence of the optimal fertility rate control was also proved by the Mazur's theorem.