Optimal birth control problems for nonlinear age-structured population dynamics

Z.-R. He; M.-S. Wang; Z.-E. Ma

doi:10.3934/dcdsb.2004.4.589

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2004, Volume 4, Issue 3: 589-594. Doi: 10.3934/dcdsb.2004.4.589

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Optimal birth control problems for nonlinear age-structured population dynamics

1.
Sciences College, Hangzhou Institute of Electronic Engineering, Hangzhou, 310018
2.
Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an, 710049

Received: September 30, 2002

Revised: June 30, 2003

Published: July 2005

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Abstract

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.

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Mathematics Subject Classification: 92D25, 49J20, 65L70.

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