Existence and asymptotic properties of solutions to elliptic systems involving multiple critical exponents  

作　　者：KANG DongSheng PENG ShuangJie 

机构地区：[1]School of Mathematics and Statistics, South-Central University For Nationalities, Wuhan 430074, China [2]School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

出　　处：《Science China Mathematics》2011年第2期243-256,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 10771219, 11071092);the PhD Specialized Grant of the Ministry of Education of China (Grant No. 20100144110001)

摘　　要：This paper is concerned with a singular elliptic system, which involves the Caffarelli-Kohn-Nirenberg inequality and multiple critical exponents. By analytic technics and variational methods, the extremals of the corresponding bet Hardy-Sobolev constant are found, the existence of positive solutions to the system is established and the asymptotic properties of solutions at the singular point are proved.This paper is concerned with a singular elliptic system, which involves the Caffarelli-Kohn-Nirenberg inequality and multiple critical exponents. By analytic technics and variational methods, the extremals of the corresponding bet Hardy-Sobolev constant are found, the existence of positive solutions to the system is established and the asymptotic properties of solutions at the singular point are proved.

关 键 词：elliptic system nontrivial solution critical exponent variational method 

分 类 号：O175.2[理学—数学] O175.25[理学—基础数学]