一类具有交叉扩散的捕食-食饵模型的分歧

摘要

The existence of positive solutions for a predator‐prey model with cross‐diffusion un‐der Dirichlet boundary condition is studied ,including some priori estimates and the existence of positive solutions .A priori estimate of positive solution is got by using maximum principle ,and the existence of positive solutions are obtained with Crandall‐Rabinowitz bifurcation theory . Finally ,the sufficient conditions for the inexistence of positive solutions of the model are ob‐tained ,and under certain conditions ,the positive solution of the model is bounded ,and a suffi‐cient condition for the existence of positive solutions from the semi‐trivial solutions are derived .%研究一类带有交叉扩散项的捕食‐食饵模型在齐次Dirichlet边界条件下解的性质，包括解的先验估计和局部分歧正解的存在性。首先利用极大值原理给出正解的先验估计；然后利用Crandall‐Rabinowitz分歧理论，得到局部分歧正解的存在性。最终得出模型的正解不存在的充分条件，以及在一定条件下模型的正解是有界的，并给出局部分歧正解存在的充分条件。