Frank, Rupert L. and König, Tobias (2019) Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent. Analysis & PDE, 12 (4). pp. 1101-1113. ISSN 1948-206X. doi:10.2140/apde.2019.12.1101. https://resolver.caltech.edu/CaltechAUTHORS:20180604-112112515
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Abstract
For n ≥ 5, we consider positive solutions u of the biharmonic equation Δ^2u = u^((n+4)/(n−4)) on R^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.
Item Type: | Article | ||||||||||||
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Alternate Title: | Classification of positive solutions to a nonlinear biharmonic equation with critical exponent | ||||||||||||
Additional Information: | © 2019 Mathematical Sciences Publishers. Received: 2 November 2017; Revised: 28 May 2018; Accepted: 30 July 2018; Published: 20 October 2018. | ||||||||||||
Subject Keywords: | fourth-order equation, critical exponent, classification, periodic solutions | ||||||||||||
Issue or Number: | 4 | ||||||||||||
Classification Code: | MSC2010: Primary: 34C25, 35B09, 35J30, 53A30 | ||||||||||||
DOI: | 10.2140/apde.2019.12.1101 | ||||||||||||
Record Number: | CaltechAUTHORS:20180604-112112515 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180604-112112515 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 86787 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Tony Diaz | ||||||||||||
Deposited On: | 04 Jun 2018 18:26 | ||||||||||||
Last Modified: | 15 Nov 2021 20:42 |
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