具有年龄结构的n种群非线性竞争系统的最优生育率控制  

Optimal birth control of n species nonlinear competition system with age-structure

作　　者：周子娟 雒志学[1] Zijuan ZHOU;Zhixue LUO(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,Gansu,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2023年第10期75-83,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11561041);甘肃省自然科学基金资助项目(1506RJZA071)。

摘　　要：研究了一类基于年龄结构的n种群非线性竞争系统的最优生育率控制问题。由不动点定理证明了系统解的存在唯一性,通过构造极值序列并运用Mazur定理证明了最优生育率控制的存在性,并利用法锥概念和共轭系统导出了需满足的必要性条件。The optimal birth control of n species nonlinear competition system with age-structure is investigated.The existence and uniqueness of non-negative solution of the system is proved by using the fixed-point theorem.The extremization sequence is constructed,and Mazur?s theorem are used to verify the existence of the optimal solution of the optimal birth control problem,and the necessity conditions are derived out via normal cone and conjugate system techniques.

关 键 词：年龄结构 竞争种群 最优生育率控制 共轭系统 法锥 

分 类 号：O175.1[理学—数学]