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Optimal contraception control for a nonlinear population model with size structure and a separable mortality

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  • This paper is concerned with the problem of optimal contraception control for a nonlinear population model with size structure. First, the existence of separable solutions is established, which is crucial in obtaining the optimal control strategy. Moreover, it is shown that the population density depends continuously on control parameters. Then, the existence of an optimal control strategy is proved via compactness and extremal sequence. Finally, the conditions of the optimal strategy are derived by means of normal cones and adjoint systems.
    Mathematics Subject Classification: Primary: 49N90; Secondary: 92D25.

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