研究了一类带Beddington—DeAngelis反应项的捕食一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.