Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity

被引：4
|
作者：
Frank, Rupert L. [1 ,2 ]
Koenig, Tobias [1 ]
机构：
[1] Ludwig Maximilans Univ Munchen, Math Inst, Theresienstr 39, D-80333 Munich, Germany
[2] CALTECH, Math Dept, Mail Code 253-37,1200 E Calif Blvd, Pasadena, CA 91125 USA
来源：
RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI | 2019年 / 30卷 / 04期
基金：
美国国家科学基金会;
关键词：
Biharmonic equation; singular solutions; method of moving planes; SOBOLEV;
D O I：
10.4171/RLM/871
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider positive solutions u of the semilinear biharmonic equation Delta(2)u = vertical bar x vertical bar(n+4/2) g(vertical bar x vertical bar(n-4/2)u) in R-n\{0} with non-removable singularities at the origin. Under natural assumptions on the nonlinearity g, we show that vertical bar x vertical bar(n-4/2)u is a periodic function of ln vertical bar x vertical bar and we classify all such solutions.
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页码：817 / 846
页数：30
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