Existence results for a super-Liouville equation on compact surfaces
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- by Aleks Jevnikar, Andrea Malchiodi and Ruijun Wu PDF
- Trans. Amer. Math. Soc. 373 (2020), 8837-8859 Request permission
Abstract:
We are concerned with a super-Liouville equation on compact surfaces with genus larger than one, obtaining the first non-trivial existence result for this class of problems via min-max methods. In particular we make use of a Nehari manifold and, after showing the validity of the Palais-Smale condition, we exhibit either a mountain pass or linking geometry.References
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Additional Information
- Aleks Jevnikar
- Affiliation: Department of Mathematics, Computer Science and Physics, University of Udine, Via delle Scienze 206, 33100 Udine, Italy
- MR Author ID: 1037775
- Email: aleks.jevnikar@uniud.it
- Andrea Malchiodi
- Affiliation: Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
- MR Author ID: 655662
- Email: andrea.malchiodi@sns.it
- Ruijun Wu
- Affiliation: Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
- MR Author ID: 1234947
- ORCID: 0000-0002-5116-713X
- Email: ruijun.wu@sns.it
- Received by editor(s): September 26, 2019
- Received by editor(s) in revised form: May 4, 2020
- Published electronically: October 5, 2020
- Additional Notes: The first and second authors were partially supported by MIUR Bando PRIN 2015 2015KB9WPT$_{001}$. They are also members of GNAMPA as part of INdAM.
The first and third authors were supported by the Centro di Ricerca Matematica ‘Ennio de Giorgi’.
The second author was partially supported by the projects Geometric problems with loss of compactness and Finanziamento a supporto della ricerca di base from Scuola Normale Superiore. - © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 8837-8859
- MSC (2010): Primary 58J05, 35A01, 58E05, 81Q60
- DOI: https://doi.org/10.1090/tran/8209
- MathSciNet review: 4177277