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中文摘要：
利用上下解方法及全藕合线性互惠系统的最大值原理,研究了一类非线性椭圆系统,给出了其正解存在的充分必要条件,同时也得到了其正解局部稳定的某些结果．
英文摘要：
In this paper we use the sub and supersolution methods and the maximum principle of the fully coupled linear cooperative systems to study a class of nonlinear elliptic cooperative system. The necessary and sufficient conditions for the existence of the positive solutions were established, and some local stability results were also obtained.
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