Double control problems of age-distributed population dynamics

This paper is concerned with some optimal control problems of an age-structured population model controlled by fecundity and culling rates. The first-order necessary optimality conditions of the following four problems are deduced by means of a Dubovitskii–Milyutin functional analysis approach: a problem with fixed horizon and terminal constraint set, a free horizon counterpart, a differential game and a mini–max problem with a non-differentiable objective functional.