| 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 |
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| 引用本文： | 黄红.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[J].南京大学学报(自然科学版),2016(2):137-151. |
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| 作者姓名： | 黄红 |
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| 作者单位： | 南京师范大学中北学院,南京,210023 |
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| 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**(s)-2u/|x|s +λf(x,u),x∈Ω,u∈H2,2(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.
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| 关 键 词： | 双调和算子 临界Sobolev-Hardy项 变分方法 紧性 |
EXISTENCE OF INFINITELY MANY SMALL SOLUTIONS FOR A CLASS OF FOURTH ORDER SINGULAR ELLIPTIC PROBLEM WITH CRITICAL SOBOLEV AND HARDY TERMS |
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| Abstract: | 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∈H2,2(Ω),N(>)5.=Employing the variational method and concentration-compactness principle,the existence of its infinitely many small solutions is proved,and the properties of its solutions are verified. |
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| Keywords: | Biharmonic operator critical Sobolev and Hardy exponent variational method compactness |
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