ON A CONTROL PROBLEM FOR A CLASS OF POPULATION SYSTEMS WITH TIME DELAY AND AGE DISTRIBUTION
一类基于时滞和年龄分布的种群控制问题

An optimal harvesting problem is considered for a class of population models with discrete delay and continuous age distribution, whose state system is described by a partial functional differential equation. The existence of optimal strategy is proved by means of maximizing sequence and Mazur's theorem, and the first-order optimality conditions are derived out via normal cone and adjoint system techniques. Finally by a detailed analysis for the adjoint system, the uniqueness and the characteristic representation of the optimal controller are given.