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2019 Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent
Rupert L. Frank, Tobias König
Anal. PDE 12(4): 1101-1113 (2019). DOI: 10.2140/apde.2019.12.1101

Abstract

For n 5 , we consider positive solutions u of the biharmonic equation

Δ 2 u = u ( n + 4 ) ( n 4 )  on  n { 0 } ,

with a nonremovable singularity at the origin. We show that | x | ( n 4 ) 2 u is a periodic function of ln | x | 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.

Citation

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Rupert L. Frank. Tobias König. "Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent." Anal. PDE 12 (4) 1101 - 1113, 2019. https://doi.org/10.2140/apde.2019.12.1101

Information

Received: 2 November 2017; Revised: 28 May 2018; Accepted: 30 July 2018; Published: 2019
First available in Project Euclid: 30 October 2018

zbMATH: 06991228
MathSciNet: MR3869387
Digital Object Identifier: 10.2140/apde.2019.12.1101

Subjects:
Primary: 34C25, 35B09, 35J30, 53A30

Rights: Copyright © 2019 Mathematical Sciences Publishers

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