具有收获率的HollingⅢ型捕食-食饵模型的平衡态

The Steady-states of Holling III Model with Constant Harvesting of Prey and Predators

研究了齐次Neumann边界条件下具有收获率的Holling Ⅲ型捕食-食饵模型的平衡态问题。首先用最大值原理和Harnack不等式给出了正解的先验估计。其次在先验估计的基础上用能量方法得到了该模型非常数正解的不存在性。最后给出了该模型非常数正解存在的充分条件,并用度理论的知识给予证明。

The steady-states of Holling Ⅲ model with constant harvesting of prey and predators subject to homogeneous Neumann boundary condition are considered.First,a priori estimates for positive solutions are established by using the maximum principle and Harnack inequality.Second,the non-existence of non-constant positive steady-states are given based on the priori estimates,in which energy method are used.Finally,some results of the sufficient conditions for non-constant positive steady-states are obtained by applying Leray-Schauder degree theory