Abstract: The reasonable harvest of biological models is closely related to the rational exploitation and utilization of resources. There are many factors that affect biological models. Most models are linear. However, many phenomena cannot be explained by linearity. In order to study this problem more truly and appropriately, this paper studies a class of nonautonomous quasilinear predator-prey models with harvesting terms. First, the upper and lower solutions of the model are constructed by using the upper and lower solutions theory of quasilinear partial differential equations with harvesting terms, and the existence of the solutions is proved. Then, the unique sufficient conditions for the existence of the solutions are found in combination with relevant lemmas and properties. Finally, the optimal harvesting amount of the model is given by using variational method. Futhermore, the numerical simulation is given by MATLAB.

Key words: quasilinear model, non-autonomyt, partial differential equation, upper and lower solutions, optimal harvest