### Optimal birth rate control for competing populations dependent on scale structure

ZHANG Ping, LUO Zhi-xue*

1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
• Published:2020-11-17

Abstract: A competitive population model with scale structure-dependent is established, and the optimal birth-control problem of the model is discussed. Firstly, the existence and uniqueness of the system solution are proved by using the characteristic line method and the Banach fixed point theorem, and the continuous dependence of the system solution on the control variables is also proved by the comparison principle. At the end of the paper, the necessity condition of the existence of optimal control is proved by using the definition of normal cone.

CLC Number:

• O715.1
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