具临界Sobolev指标的奇异椭圆方程在R^N上解的存在性  

The Existence of Solutions for a Singular Elliptic Equation Involving Critical Sobolev Exponent in R^N

作　　者：张丹丹[1] 

机构地区：[1]襄樊学院数学系,湖北襄樊441053

出　　处：《襄樊学院学报》2007年第8期13-17,共5页Journal of Xiangfan University

摘　　要：文章克服了无界域上嵌入H r1(R N)→L2*(RN)的非紧性困难及μ≠0时解的奇性问题,运用没有(PS)c条件的山路引理证明了一类具有临界Sobolev和Hardy指标的椭圆型方程的非平凡解的存在性问题.For the critical case, there are some difficulties when trying to find the nontrivial solution by variational methods because the embedding H r1 (RN) → L2 *(RN)is not compact and the singularity of solution for μ ≠ 0. This paper is concerned with the existence of the nontrivial solutions for an elliptic equation involving critical Sobolev and Hardy exponents. By using Mountain Pass theorem without (PS)c condition we get the main results.

关 键 词：临界SOBOLEV指标 临界Hardy指标 临界点 (PS)c条件 

分 类 号：O175.25[理学—数学]