一类捕食-被捕食模型的正平衡解存在性

Existence of Positive Solutions of a Predator-Prey Model

针对自然界中捕食者染病的现象,建立了捕食者染病的捕食-被捕食模型,研究了捕食者为躲避疾病进行扩散,并且具有HollingⅡ功能性反应函数和齐次Neumann边界条件的问题,利用Harnack不等式和最大值原理给出反应扩散问题的正平衡解的先验估计,并利用拓扑度理论证明该问题的非常数正平衡解的存在性.讨论了对应平衡态问题的非常数正平衡解存在性。

In the view of the phenomenon that the predator is sick,a predator-prey model with an epidemic in the predator is considered. A system with diffnsion and a Holling type II function under the homogeneous Neumann boundary condition is studied,the existence for a steady state of the corresponding steady state problem is discussed.First,discuss the condition of the development of the field and introduce the theorems; Secondly, a prior estimates of the positive steady states of the reaction-diffusion system is given by the Harnack inequation and maximum principle;Finally, the existence of non-constant positive steady state is obtained by using the topological degree.