中文摘要：

研究了一类带有交叉扩散的捕食-食饵模型在齐次Dirichlet边界条件下正解的存在性.利用极大值原理得到正解的先验估计;通过分析相关特征值问题,得到两条无界的中性曲线;最后以食饵生长率为分歧参数,借助Crandall-Rabinowitz分歧理论,得出局部分歧正解的存在性.

英文摘要：

The existence of positive solutions for a predator-prey model with cross-diffusion under homo-geneous Dirichlet boundary conditions is studied .By the maximum principle ,some apriori estimates of positive solution are obtained .Then ,by considering the related eigenvalue problems ,two unbounded neutral curves are given .Finally ,using Crandall-Rabinowitz bifurcation theory ,with the grow th rate of prey as a bifurcation parameter ,the positive solutions is emanated from the semi-trivial solutions are de-rived .