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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. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190520-133342030

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Abstract

We consider positive solutions u of the semilinear biharmonic equation Δ2^u = |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:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1903.02385arXivDiscussion Paper
ORCID:
AuthorORCID
Frank, Rupert L.0000-0001-7973-4688
Additional Information:© 2019 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. 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
Record Number:CaltechAUTHORS:20190520-133342030
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190520-133342030
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:20 May 2019 20:37

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