Theoretical results of optimal harvesting in a hierarchical size-structured population system with delay

We investigate an optimal control problem for a hierarchical size-structured population model, which incorporates the inoculation delay into the globally feedbacked boundary condition. After the establishment of the continuity of the states with respect to the harvesting efforts, the existence of the optimal solutions is proved by a result in convex analysis, and the maximum principle is obtained via conjugate system and tangent-normal cones.