中文摘要：

研究了一个带混合边界条件和扩散作用的比率依赖捕食模型，其中食物带第二类边值，而捕食者带第三类边值．利用指数理论、度理论和逼近方法，我们获得了当a〉m1且b〉d2λ1：或d2λ1-m2〈b〈d2λ1时对应的捕食模型至少存在一个正稳态解．

英文摘要：

This paper investigates a ratio-dependent predator-prey model with diffusion in which the predator is subject to the homogeneous Robin boundary condition and the prey to the homogeneous Neumann boundary condition. By making use of the index theory, topologic degree theory and the approximation methods, we obtain that the model at least possesses a positive steady-state solution when a 〉 m1 and b 〉 d2λ1, or d2λ1 - m2 〈 b 〈 d2λ1.