CaltechAUTHORS
  A Caltech Library Service

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

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. https://resolver.caltech.edu/CaltechAUTHORS:20180604-112112515

[img] PDF - Published Version
See Usage Policy.

567Kb
[img] PDF - Submitted Version
See Usage Policy.

217Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20180604-112112515

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
Related URLs:
URLURL TypeDescription
https://doi.org/10.2140/apde.2019.12.1101 DOIArticle
https://projecteuclid.org/euclid.apde/1540864862PublisherArticle
https://arxiv.org/abs/1711.00776arXivDiscussion Paper
ORCID:
AuthorORCID
Frank, Rupert L.0000-0001-7973-4688
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
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:03 Oct 2019 19:48

Repository Staff Only: item control page