American Institute of Mathematical Sciences

Advanced
August  2004, 4(3): 589-594. doi: 10.3934/dcdsb.2004.4.589

Optimal birth control problems for nonlinear age-structured population dynamics

Z.-R. He 1, , M.-S. Wang 2, and  Z.-E. Ma 2,

1. 

Sciences College, Hangzhou Institute of Electronic Engineering, Hangzhou, 310018, China
2. 

Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an, 710049, China, China

Received  October 2002 Revised  July 2003 Published  May 2004

We study the least cost-size problem and the least cost-deviation problem for a nonlinear population model with age-dependence, which takes fertility rate as the control variable. The existence of a unique optimal control and the optimality conditions of first order are investigated by means of Ekeland's variational principle and normal cone technique. Our conclusion extends a known result in the literature.
Keywords: Ekeland variational principle., population model, optimal control, Age-structure.
Mathematics Subject Classification: 92D25, 49J20, 65L7.
Citation: Z.-R. He, M.-S. Wang, Z.-E. Ma. Optimal birth control problems for nonlinear age-structured population dynamics. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 589-594. doi: 10.3934/dcdsb.2004.4.589
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