中文摘要：

研究了一类具有扩散和交叉扩散项的Holling—Tanner捕食-食饵模型．首先利用最大值原理和Harnack不等式给出正解的先验估计，进一步利用度理论得到非常数正解的存在性与不存在性，从而给出非常数正解存在的充分条件．

英文摘要：

This paper will discuss a Holling-Tanner predator-prey ecological model with diffusion and cross-diffusion. By means of maximum principle and Harnack inequality, a priori estimates are first established. Furthermore, the degree theory is utilized to obtain the existence and non-existence of non-constant positive solutions. The results indicate that non-constant positive solutions are created under some conditions.