含临界耦合非线性项的奇异椭圆方程组的非平凡解  

Nontrivial Solutions for Singular Elliptic Systems Involving Critical Coupling Nonlinear Terms

作　　者：徐国进[1] 吕登峰[1] 

机构地区：[1]湖北工程学院数学与统计学院,湖北孝感432000

出　　处：《西南大学学报（自然科学版）》2012年第8期104-107,共4页Journal of Southwest University(Natural Science Edition)

基　　金：湖北省教育厅重点科研项目(D20122605);湖北工程学院青年项目(Z2012003)

摘　　要：研究了有界区域上一类含Sobolev临界指数与奇异位势的带权椭圆方程组,通过Caffarelli-Kohn-Nirenberg不等式与精确的能量估计,并运用山路引理得到了这类方程组非平凡解的存在性.This paper deals with a class of weighted nonlinear elliptic systems involving Sobolev critical exponents and singular potentials in bounded domains.By using the Caffarelli-Kohn-Nirenberg inequality and delicate energy estimates,the existence of their nontrivial solutions is obtained by exploiting the mountain pass theorem.

关 键 词：非平凡解 椭圆方程组 SOBOLEV临界指数 Caffarelli-Kohn-Nirenberg不等式 

分 类 号：O175.25[理学—数学]