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 | |||||||||
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| 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. | |||||||||
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| 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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