# American Institute of Mathematical Sciences

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

## Optimal birth control problems for nonlinear age-structured population dynamics

 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.
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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