含多奇性临界双调和椭圆型问题解的存在性(英文)  

The Existence for the Solutions of the Critical Biharmonic Elliptic Equation with Multi-singularity

作　　者：熊辉[1] 

机构地区：[1]东莞理工学院 软件学院,广东东莞523808

出　　处：《东莞理工学院学报》2007年第3期1-7,共7页Journal of Dongguan University of Technology

基　　金：Supported by NNSF of China(NO.1037116).

摘　　要：摘要:文章主要在有界域Ω中研究了如下含多奇性的半线形椭圆型问题其中N≥5,k∈N,(λ_1,λ_1,…,λ_k)∈R^k,(a_1,a_2,…,a_k)∈R^(kN)且2~*=2N/N-4是临界的嵌入指数,由于Sobolev嵌入失去紧性,所以文章将通过集中紧原理得到正解的存在性．This paper mainly studied the sernilinear biharmonic elliptic equation with multi-singularity and critical exponent, in whichwe {△^2u=^4∑t=1 λu｜x-a1｜4＋u^2＊-1,x∈Ω u=au/av=0,x∈aΩ u〉0,x∈Ω/{a1,…,an} mainly studied, where N≥5,k∈N,（λ1,λ2,…λk）∈R^K,（a1,a2,…,ak）∈R^kN and 2^＊=2N/N-4 i is the critical Sobolev exponent. For the loss of the compactness of the embedding, the concentrated compactness principle was adopted to obtain the existence of the positive solution.

关 键 词：双调和 多奇性 临界指数 

分 类 号：O175.25[理学—数学]