带交叉扩散项的捕食模型非常数正解的存在性

The Existence of Nonconstant Positive Solution for a Prey-Predator Model with Cross-Diffusion

讨论了一类具有交叉扩散项的捕食食饵模型正解的存在性。利用最大值原理和Harnack不等式给出了模型正解的先验估计,运用积分性质证明了非常数正解的不存在性,再利用度理论得到了非常数正解存在的充分条件。

The existence of positive solutions is discussed for a prey-predator model with cross-diffusion.The prior estimate to the positive solutions of the model is given by means of maximum principle and Harnack inequality.By using the integral property,the nonexistence of the nonconstant positive solutions is proved.The sufficient conditions for the existence of nonconstant positive solutions are obtained.