CAJ | 학술논문

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。
재제차Dirichlet변계조건하연구일류충내상식적포식-식이모형정해적존재성화유일성。수선이용겁치원리、상하해방법급출정해적선험고계，연후이용Leray-Schauder도이론，통과계산추영사불동점지표득도정해적존재성，최후이용특정치변분원리급출정해존재적유일성。
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.