@article{Liu2025, 
author = {Rong Liu and Xin Yi and Yanmei Wang},
title = {Optimal development problem for a nonlinear population model with size structure in a periodic environment},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {5},
pages = {12726-12744},
keywords = {environmental periodicity, size structure, optimal harvesting, nonlinear recruitment process},
url = {https://www.sciopen.com/article/10.3934/math.2025573},
doi = {10.3934/math.2025573},
abstract = {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.}
}