Optimal harvesting control problem for linear periodic age-dependent population dynamics

摘要

In this paper, we investigate an optimal harvesting problem for linear periodic age-dependent population dynamics. Namely, we consider the Lotka–Mckendrick model with periodic vital rates and a periodic forcing term that sustains oscillations. By Mazur's Theorem, we demonstrate existence of solutions of the optimal control problem (OH) and by the conception of normal cone, we also obtain the first order necessary conditions of optimality for problem (OH). Finally, under suitable assumptions, we give uniqueness of solutions of the optimal control problem (OH). Our results extend some known criteria.