Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent

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.

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Keywords

fourth-order equation, critical exponent, classification, periodic solutions

Mathematical Subject Classification 2010

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

Milestones

Received: 2 November 2017

Revised: 28 May 2018

Accepted: 30 July 2018

Published: 20 October 2018

Authors

Rupert L. Frank
Mathematisches Institut Ludwig-Maximilians-Universität München München Germany	Department of Mathematics Caltech Pasadena, CA United States

Tobias König
Mathematisches Institut Ludwig-Maximilians-Universität München München Germany

Vol. 12, No. 4, 2019

Rupert L. Frank and Tobias König

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors