中文摘要：

研究了一类具有HollingⅢ型捕食-食饵模型平衡态正解的存在性与稳定性.利用锥上的不动点理论给出正解存在的充分条件;讨论了m充分大时,借助上下解方法构造出模型的正解,并根据线性稳定性理论讨论了该正解的稳定性.结果表明：当参数a＞λ1,c＞λ1（-dθ2α/1＋mθ2α）时,共存解存在,且当c＞λ1时,共存解是线性稳定的.

英文摘要：

Abstract： The existence and stability of positive solutions are investigated for a predator-prey model with Holling type [[[ functional response. By using the fixed point index in cones, one can reduce the sufficient conditions for any possible positive solutions. When m is suitably large,by the super-sub solution method for predator-prey systems, the positive solutions and the stability of the positive solutions are studied by using the linearized stability. It is shown that the models a〉λ1,c〉λ1（-dθ2α/1＋mθ2α）md the coexistence solution is linear sta-bility if c〉λ1