Periodic optimal control for competing parabolic Volterra-Lotka-type systems

In this paper, we study the optimal harvesting control problem governed by a time-periodic competing parabolic Volterra-Lotka system. We show the existence of an optimal control, and we also find some conditions which enable the characterization of the optimal control in terms of a large parabolic optimality system. We further construct monotone sequences closing in to all appropriate solutions of the periodic optimality system.

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