中文摘要：

研究带Dirichlet边界条件的强耦合问题共存解，采用上、下解方法并结合相应的单调迭代序列方法，给出了共存解的充分条件：当交错扩散和种群间作用相对较弱时，强耦合系统至少有一个正解存在．

英文摘要：

This paper deals with the existence of positive solutions to a strongly coupled system with homogeneous Dirichlet boundary conditions. Using the upper and lower solutions as well as its associated monotone iterations, sufficient conditions are given for the system to have a coexistence.The results show that this model possesses at least one coexistence state if cross-diffusions are weak.