中文摘要：

在齐次Dirichlet边界条件下研究一类种内相食的捕食-食饵模型正解的存在性和惟一性。首先利用极值原理、上下解方法给出正解的先验估计，然后利用Leray—Schauder度理论，通过计算锥映射不动点指标得到正解的存在性，最后利用特征值变分原理给出正解存在的惟一性。

英文摘要：

Under homogeneous Dirichlet boundary conditions, a predator-prey model with predator cannibalism is con- sidered. The existence and uniqueness of positive solutions are presented. By maximum principles and lower-upper solu-tion methods, a prior estimate of positive solutions is firstly obtained. Then by Leray-Schauder theory and resorting to calculate fixed point indices of compact maps in cones, sufficient conditions for coexistence are given. Moreover, the u-niqueness of positive solutions is derived under some conditions.