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Classification of
positive singular solutions to a nonlinear biharmonic
equation with critical exponent
Rupert L. Frank and Tobias König |
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Vol. 12 (2019), No. 4, 1101–1113
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DOI: 10.2140/apde.2019.12.1101
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Abstract |
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For , we consider positive solutions of the biharmonic equation with a nonremovable singularity at the origin. We show that is a periodic function of 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 -curvature problem in conformal geometry. |
Keywords
fourth-order equation, critical exponent, classification,
periodic solutions
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Mathematical Subject Classification 2010
Primary: 34C25, 35B09, 35J30, 53A30
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Milestones
Received: 2 November 2017
Revised: 28 May 2018
Accepted: 30 July 2018
Published: 20 October 2018
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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 |
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