Optimal development problem for a nonlinear population model with size structure in a periodic environment

This paper investigated the optimal development problem of a size-structured population model under a periodic environmental setting. The boundary condition of the novel model consists of a nonlinear recruitment process and a bounded input, which endow the model with more realistic and complex characteristics compared to traditional ones. First, we established the existence of a unique non-negative bounded solution and demonstrated the continuous dependence of the solutions on the control variable. Next, we showed that the adjoint system is also well-posed. Then, the Euler-Lagrange equations describing the exact structure of the optimal strategies were derived and the existence of a unique optimal policy was proved. Finally, some numerical results were presented. The obtained research results will contribute to the development of some renewable resources, such as fish resources.