| 年龄相关的种群系统的最优生育率控制 |
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| 引用本文： | 李健全,陈任昭. 年龄相关的种群系统的最优生育率控制[J]. 生物数学学报, 2006, 21(2): 191-203 |
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| 作者姓名： | 李健全 陈任昭 |
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| 作者单位： | 1. 华南师范大学,数学系,广东,广州,510631
2. 东北师范大学,数学系,吉林,长春,130024 |
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| 基金项目： | 广东省自然科学基金资助项目(031496)，华南师范大学博士启动基金资助项目(670070) |
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| 摘 要： | 讨论了一类与年龄相关的时变种群系统最优生育率控制的非线性问题,利用Ba- nach空间的Saks-Masur引理,证明了系统最优生育率控制的存在唯一性,并得到了控制为最优的必要条件和最优性组．所得结果可为种群系统控制问题的实际研究提供必要的数学理论基础．
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| 关 键 词： | 年龄相关 时变种群系统 最优生育率控制 必要条件 最优性组 |
| 文章编号： | 1001-9626（2006）02-0191-13 |
| 收稿时间： | 2004-09-21 |
| 修稿时间： | 2004-09-21 |
Optimal Fertility Rate Control for Age-Dependent Population System |
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| LI Jian-quan,CHEN Ren-zhao. Optimal Fertility Rate Control for Age-Dependent Population System[J]. Journal of Biomathematics, 2006, 21(2): 191-203 |
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| Authors: | LI Jian-quan CHEN Ren-zhao |
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| Affiliation: | 1 Department of Mathematics, South China Normal University, Guangzhou Guangdong 510631 China;2 Department of Mathematics, Northeast Normal University, Changchun Jilin 130024 China |
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| Abstract: | This paper discusses the optimal fertility rate control problem for a class of time-varying age-dependent population system. It proves the existence and uniqueness of the optimal fertility rate control and obtains the necessary conditions for a control to be optimal and its optimality systems determining optimal controls. These results obtained may provide a strict mathematical theoretical basis for the pratical study of the control problems in population systems. |
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| Keywords: | Age-dependent population system Optimal fertility rate control Necessary conditions Optimality system |
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