一类含临界耦合非线性项的奇异椭圆方程组的正解  

POSITIVE SOLUTION FOR A CLASS OF SINGULAR ELLIPTIC SYSTEMS WITH CRITICAL COUPLING NONLINEAR TERMS

作　　者：吕登峰[1] 

机构地区：[1]孝感学院数学与统计学院,湖北孝感432000

出　　处：《数学杂志》2012年第2期357-362,共6页Journal of Mathematics

基　　金：国家自然科学基金资助项目(10631030);孝感学院青年项目(z2011004)

摘　　要：本文研究了一类含临界指数与耦合非线性项的奇异椭圆方程组. 利用变分方法与极大值原理, 通过证明对应的能量泛函满足局部的 (PS)c 条件, 得到了这类方程组正解的存在性, 推广了单个方程与方程组中的相应结果.In this paper,we study a class of singular elliptic systems involving critical exponents and coupling nonlinear terms.By using the variational methods and strong maximum principle and estimating the energy functional corresponding to the problem satisfying the local（PS）c condition,we prove the existence of at least one pair of positive solutions for the elliptic systems.The conclusions of this paper extend the corresponding results of single equation and system of equations.

关 键 词：椭圆方程组 临界指数 Hardy项 正解 

分 类 号：O175.25[理学—数学]