一类含有临界Sobolev-Hardy项的四阶奇异椭圆方程无穷多小解的存在性（英文）  

EXISTENCE OF INFINITELY MANY SMALL SOLUTIONS FOR A CLASS OF FOURTH ORDER SINGULAR ELLIPTIC PROBLEM WITH CRITICAL SOBOLEV AND HARDY TERMS

作　　者：黄红[1] Huang Hong(Zhongbei College, Nanjing Normal University, 210023 Nanjing)

机构地区：[1]南京师范大学中北学院,南京210023

出　　处：《南京大学学报（数学半年刊）》2016年第2期137-151,共15页Journal of Nanjing University(Mathematical Biquarterly)

摘　　要：本文研究了一类含有临界Sobolev-Hardy项的四阶奇异椭圆方程问题△~2u=μ(|u|^(2**(a)-2))/(|x|~8)+λf(x,u),x∈ΩH_0^(2,2)(Ω),N≥5利用变分方法和集中紧性原理,证明了该四阶奇异椭圆方程问题无穷多小解的存在性.We investigate a class of fourth order elliptic problem which is singular potential and involves critical Sobolev and Hardy terms.△^2u=μ｜u｜2^＊＊（s）-2u/｜x｜s＋λf（x,u）,x∈Ω,u∈H0^2,2（Ω）,N≥5.Employing the variational method and concentration-compactness principle, the exis- tence of its infinitely many small solutions is proved, and the properties of its solutions are verified.

关 键 词：双调和算子 临界Sobolev-Hardy项 变分方法 紧性 

分 类 号：O175.25[理学—数学]