带有交叉扩散项的Holling-typeⅡ捕食-食饵模型的共存

Stationary patterns for a prey-predator model with Holling type Ⅱ functional response and density-dependent diffusion term

讨论了带有交叉扩散项的Holling-typeⅡ反应项的捕食-食饵模型在齐次Neumann边界条件下非常数正解的存在性.首先利用最大值原理、上下解方法和Harnack不等式对正解的上下界做了先验估计;其次在先验估计的基础上运用Leray-Schauder度理论证明非常数正解的存在性,并给出了正解存在的充分条件.

A predator-prey model with Holling type Ⅱ functional response and Density-Dependent Diffusion Term under homogeneous Neumann boundary condition are discussed.First,by the maximum principle,the lower-upper solution method and Harnack inequality,a priori estimate for upper and lower bounds is discussed.Second,the sufficient conditions for the existence of steady-state solutions are obtained by the priori upper and lower bounds and Leray-Schauder degree theory.