Optimal harvesting control of N species for a nonlinear population system

Abstract

In this paper, we investigate the optimal harvesting problem for a class of nonlinear population system with fertility and mortality depending on the population size. Fixed point theory is used to obtain the existence and uniqueness of nonnegative solution in terms of the controls. Optimality conditions are derived by means of normal cone technique. The existence of the optimal control is carefully verified via Ekeland's variation principle, some results in references are extended.