具有Sobolev临界指数的半线性椭圆方程的正解(英文)  

Positive solutions for semilinear elliptic equations with critical Sobolev exponents

作　　者：郭千桥[1] 崔学伟[1] 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《中国科学院研究生院学报》2009年第2期158-166,共9页Journal of the Graduate School of the Chinese Academy of Sciences

基　　金：supported by Natural Science Basic Research Planin Shaanxi Province of China(2006A09)

摘　　要：在Rn中具有光滑边界的有界域Ω内考虑具有Dirichlet边界条件的半线性椭圆方程-Δu-μ|xu|2=g(x,u)+|u|2*-2u,这里g(x,.)在无穷远处具有次临界增长.由变分法,利用Brzis和Nirenberg"Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents.Comm.Pure Appl.Math.1983,36:437～477"的思想,证明了正解的存在性.We consider the following semilinear elliptic equation -Δu-μ｜xu｜2=g（x,u）＋｜u｜2＊-2u in Ω with Dirichlet boundary condition, where g （x,.） has subcritical growth at infinity. The existence of positive solutions are obtained by variational method in the spirit of Brezis-Nirenberg.

关 键 词：SOBOLEV临界指数 HARDY位势 山路引理 

分 类 号：O175.25[理学—数学]