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

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.