一类与Cafiarelli-Kohn-Nirenberg不等式有关的奇异椭圆型方程组
ON A SINGULAR ELLIPTIC SYSTEM INVOLVING THE CAFFARELLI-KOHN-NIRENBERG INEQUALITY

本文研究了一类与Cafiarelli-Kohn-Nirenberg不等式有关的带临界指数的奇异椭圆型方程组.利用变分方法，证明了方程组的正解及变号解的存在性.结果部分推广了文献[19]的结果.
In this paper, we consider a singular elliptic system which involves critical exponent and the well-known Cafiarelli-Kohn-Nirenberg inequality. By virtue of variational methods, we establish the existence of positive solution and sign-changing solution to the system, which partially extend the results in[19]