Abstract: The existence and stability of positive steady state solutions for a competition model with diffusion are studied under Dirichlet boundary condition. By using bifurcation theory and standard elliptic equations regularity theory, the existence of bifurcation solutions for steady state is analyzed. The sufficient condition of the existence is obtained and is verified by the numerical simulations. By the linear stability theory, the stable condition of bifurcation solutions is given. The research results show that the system can reach the stable coexistence state when the parameters satisfy certain conditions.

Key words: Dirichlet boundary, competition model, bifurcation solution, stability

摘要： 在Dirichlet边界条件下研究了一类具有扩散的两物种竞争模型平衡态正解的存在性和稳定性。运用分歧理论和标准的椭圆型方程正则性理论分析了平衡态分歧解的存在性，得到了其存在的充分条件，并通过数值模拟验证了该条件。利用线性稳定性理论得到了分歧解稳定的条件。研究结果表明，当参数满足一定条件时，系统达到稳定的共存态。

关键词: Dirichlet边界, 竞争模型, 分歧解, 稳定性