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Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity

Frank, Rupert L. and König, Tobias (2019) Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity. Rendiconti Lincei - Matematica e Applicazioni, 30 (4). pp. 817-846. ISSN 1120-6330. https://resolver.caltech.edu/CaltechAUTHORS:20190520-133342030

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Abstract

We consider positive solutions u of the semilinear biharmonic equation Δ²u = |x|−^(n+4)/2g(|x|^(n−4)/2u) in R^n∖{0} with non-removable singularities at the origin. Under natural assumptions on the nonlinearity g, we show that |x|^(n−4)/2u is a periodic function of ln|x| and we classify all such solutions.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.4171/RLM/871DOIArticle
https://arxiv.org/abs/1903.02385arXivDiscussion Paper
ORCID:
AuthorORCID
Frank, Rupert L.0000-0001-7973-4688
Additional Information:© 2019 EMS Publishing House. Published online: 2019-11-05. Partial support through US National Science Foundation grant DMS-1363432 (R.L.F.) and Studienstiftung des deutschen Volkes (T.K.) is acknowledged.
Funders:
Funding AgencyGrant Number
NSFDMS-1363432
Studienstiftung des deutschen VolkesUNSPECIFIED
Subject Keywords:Biharmonic equation, singular solutions, method of moving planes
Issue or Number:4
Record Number:CaltechAUTHORS:20190520-133342030
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190520-133342030
Official Citation:Frank Rupert, König Tobias: Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 30 (2019), 817-846. doi: 10.4171/RLM/871
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95605
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 May 2019 20:37
Last Modified:04 Dec 2019 17:09

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