A note on solutions of Yamabe-type equations on products of spheres
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- by Jimmy Petean and Héctor Barrantes González PDF
- Proc. Amer. Math. Soc. 147 (2019), 3143-3153 Request permission
Abstract:
We consider Yamabe-type equations on the Riemannian product of constant curvature metrics on $\mathbf {S}^n \times \mathbf {S}^n$ and study solutions which are invariant by the cohomogeneity one diagonal action of $O(n+1)$. We obtain multiplicity results for both positive and nodal solutions. In particular we prove the existence of nodal solutions of the Yamabe equation on these products which depend non-trivially on both factors.References
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Additional Information
- Jimmy Petean
- Affiliation: Centro de Investigación en Matemáticas, CIMAT, Calle Jalisco s/n, 36023 Guana- juato, Guanajuato, México
- MR Author ID: 626122
- Email: jimmy@cimat.mx
- Héctor Barrantes González
- Affiliation: Centro de Investigación en Matemáticas, CIMAT, Calle Jalisco s/n, 36023 Guana- juato, Guanajuato, México; Universidad de Costa Rica, Sede de Occidente, 20201, Alajuela, Costa Rica
- Email: hector.barrantes@cimat.mx, hector.barrantes@ucr.ac.cr
- Received by editor(s): September 28, 2018
- Published electronically: March 21, 2019
- Additional Notes: J. Petean is supported by grant 220074 of Fondo Sectorial de Investigación para la Educación SEP-CONACYT
- Communicated by: Jia-Ping Wang
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3143-3153
- MSC (2010): Primary 53-06, 53C21, 53C99, 58B20, 58J05
- DOI: https://doi.org/10.1090/proc/14478
- MathSciNet review: 3973913