一类捕食-食饵模型正解的存在性和惟一性

一类捕食-食饵模型正解的存在性和惟一性 Existence and Uniqueness of Positive Solutions for a Kind of Predator-Prey Model 郭改慧 GUO Gaihui 1 2 first-author 吴建华 WU Jianhua 1 2 陕西师范大学数学与信息科学学院 陕西师范大学数学与信息科学学院 College of Mathematics and Information Science, Shaanxi Normal University College of Mathematics and Information Science, Shaanxi Normal University 陕西师范大学数学与信息科学学院,陕西,西安,710062 陕西师范大学数学与信息科学学院,陕西,西安,710062 研究了一类带Beddington-DeAngelis反应项的捕食-食饵模型的平衡态问题,给出了正解的存在性和惟一性.利用Leray-Schauder度理论,通过计算锥映射不动点指标,结合极值原理、上下解方法,得到了正解存在的充分条件.并且,利用特征值变分原理给出了正解存在的惟一性条件. The steady-state of the predator-prey model with Beddington-DeAngelis functional response is studied. The existence and uniqueness of positive solutions are presented. By means of fixed point index of compact maps in cones, combining with maximum principles and lower-upper solution methods, sufficient conditions for coexistence are obtained. Moreover, the uniqueness is derived under some conditions. Beddington-DeAngelis反应项 不动点指标 存在性 惟一性 Beddington-DeAngelis functional response fixed point index existence uniqueness O175 国家自然科学基金资助项目（10571115） 2008-01-01 2021-04-01 1