CLASSIFICATION OF POSITIVE SINGULAR SOLUTIONS TO A NONLINEAR BIHARMONIC EQUATION WITH CRITICAL EXPONENT

被引：32

作者：

Frank, Rupert L. ^{[1
,2
]}

Koenig, Tobias ^{[1
]}

机构：

[1] Ludwig Maximilians Univ Munchen, Math Inst, Munich, Germany

[2] CALTECH, Dept Math, Pasadena, CA 91125 USA

来源：

ANALYSIS & PDE | 2019年 / 12卷 / 04期

基金：

美国国家科学基金会;

关键词：

fourth-order equation; critical exponent; classification; periodic solutions; SCALAR CURVATURE METRICS; DIFFERENTIAL-EQUATIONS; WEAK SOLUTIONS; SOBOLEV; REGULARITY; BEHAVIOR;

D O I：

10.2140/apde.2019.12.1101

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For n >= 5, we consider positive solutions u of the biharmonic equation Delta(2)u = u((n+4)/(n-4)) on R-n \ {0}, with a nonremovable singularity at the origin. 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 periodic functions obtained in this way. This result is relevant for the description of the asymptotic behavior of local solutions near singularities and for the Q-curvature problem in conformal geometry.

引用

页码：1101 / 1113

页数：13

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