中文摘要：

讨论了一类带有Crowley-Martin反应函数的具有一个食饵和两个捕食者的捕食－食饵模型正解的存在性和持久性。首先利用空间分解和隐函数定理研究了系统的二重分歧，得到了正平衡解存在的充分条件。其次给出了系统正平衡解不存在的充分条件。最后讨论了抛物系统正解的渐近行为，利用比较原理给出了系统持久和灭绝的充分条件。

英文摘要：

The existence and permanence of the positive solutions for a one-prey and two-predators model with Crowley-Martin type functional response are considered. First, the bifurcation from a double eigen- value for system is discussed by virtue of the space decomposition and the implicit function theorem, and the sufficient conditions for the existence of the positive steady-state solutions are obtained. Moreover, the sufficient conditions for the non-existence of the positive steady-state solutions are given. Finally, asymp- totic behavior of the positive solutions of the parabolic system is investigated, and the sufficient conditions for extinction and permanence of the parabolic system are given by using the comparison theorem.