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中文摘要：
讨论了一类推广的竞争生态模型的平衡态系统在第三边界条件下正解的存在性和稳定性.利用极值原理得到半平凡解（u0,0）,（0,v0）的存在惟一性,利用局部分歧的技巧证明了系统在（u0,0）（0,v0）处出现分歧现象,从而得到正解分支.然后利用线性算子扰动理论和分支解的稳定性理论得到这类正解的稳定性.
英文摘要：
The existence and stability on a kind of strictly positive solutions of the steady-state system are investigated for a class of extended competition biological system under the third boundary conditions. Using the maximum principle, the existence and uniqueness of two class of semi-trivial solutions are obtained. By means of local bifurcation theories ,the system generate bifurcations at the points （u0 ,0）, （0 ,v0 ） ,and the positive solutions bifurcations are proved. Furthermore partial stability for the positive solutions is established by the perturbation theorem for linear operators and the stability theorem for bifurcation solutions.
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