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A note on solutions of Yamabe-type equations on products of spheres


Authors: Jimmy Petean and Héctor Barrantes González
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
Published electronically: March 21, 2019
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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.


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Additional Information

Jimmy Petean
Affiliation: Centro de Investigación en Matemáticas, CIMAT, Calle Jalisco s/n, 36023 Guana- juato, Guanajuato, México
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

DOI: https://doi.org/10.1090/proc/14478
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
Article copyright: © Copyright 2019 American Mathematical Society