Published 2019
| Published + Submitted
Journal Article
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Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent
- Creators
- Frank, Rupert L.
- König, Tobias
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.
Additional Information
© 2019 Mathematical Sciences Publishers. Received: 2 November 2017; Revised: 28 May 2018; Accepted: 30 July 2018; Published: 20 October 2018.Attached Files
Published - apde-v12-n4-p08-s.pdf
Submitted - 1711.00776.pdf
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Additional details
- Alternative title
- Classification of positive solutions to a nonlinear biharmonic equation with critical exponent
- Eprint ID
- 86787
- Resolver ID
- CaltechAUTHORS:20180604-112112515
- Created
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2018-06-04Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field