Doubling the equatorial for the prescribed scalar curvature problem on SN

Lipeng Duan; Monica Musso; Suting Wei

doi:10.1007/s00030-023-00845-z

Doubling the equatorial for the prescribed scalar curvature problem on S^N

Lipeng Duan, Monica Musso, Suting Wei

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

6 Citations (SciVal)

Abstract

We consider the prescribed scalar curvature problem on S^NΔSNv-N(N-2)2v+K~(y)vN+2N-2=0onSN,v>0inSN,under the assumptions that the scalar curvature K~ is rotationally symmetric, and has a positive local maximum point between the poles. We prove the existence of infinitely many non-radial positive solutions, whose energy can be made arbitrarily large. These solutions are invariant under some non-trivial sub-group of O(3) obtained doubling the equatorial. We use the finite dimensional Lyapunov–Schmidt reduction method.

Original language	English
Article number	40
Journal	Nonlinear Differential Equations and Applications
Volume	30
Issue number	3
DOIs	https://doi.org/10.1007/s00030-023-00845-z
Publication status	Published - 21 Mar 2023

Funding

L. Duan was supported by the China Scholarship Council and NSFC grant (No.11771167, No.12201140), Technology Foundation of Guizhou Province ([2001]ZK008) and Guangdong Basic and Applied Basic Research Foundation (No. 2022A1515111131). M. Musso was supported by EPSRC research Grant EP/T008458/1. S. Wei was supported by the NSFC Grant (No.12001203) and Guangdong Basic and Applied Basic Research Foundation (No. 2020A1515110622). Some part of the work was done during the visit of L. Duan to Prof. M. Musso at the University of Bath. L. Duan would like to thank the Department of Mathematical Sciences for its warm hospitality and supports.

Keywords

Finite dimensional Lyapunov–Schmidt reduction
Lyapunov–Schmidt reduction
Prescribed scalar curvature problem
Scalar curvature problem

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s00030-023-00845-zLicence: CC BY

Cite this

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title = "Doubling the equatorial for the prescribed scalar curvature problem on SN",

abstract = "We consider the prescribed scalar curvature problem on SNΔSNv-N(N-2)2v+K~(y)vN+2N-2=0onSN,v>0inSN,under the assumptions that the scalar curvature K~ is rotationally symmetric, and has a positive local maximum point between the poles. We prove the existence of infinitely many non-radial positive solutions, whose energy can be made arbitrarily large. These solutions are invariant under some non-trivial sub-group of O(3) obtained doubling the equatorial. We use the finite dimensional Lyapunov–Schmidt reduction method.",

keywords = "Finite dimensional Lyapunov–Schmidt reduction, Lyapunov–Schmidt reduction, Prescribed scalar curvature problem, Scalar curvature problem",

author = "Lipeng Duan and Monica Musso and Suting Wei",

year = "2023",

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doi = "10.1007/s00030-023-00845-z",

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T1 - Doubling the equatorial for the prescribed scalar curvature problem on SN

AU - Duan, Lipeng

AU - Musso, Monica

AU - Wei, Suting

PY - 2023/3/21

Y1 - 2023/3/21

N2 - We consider the prescribed scalar curvature problem on SNΔSNv-N(N-2)2v+K~(y)vN+2N-2=0onSN,v>0inSN,under the assumptions that the scalar curvature K~ is rotationally symmetric, and has a positive local maximum point between the poles. We prove the existence of infinitely many non-radial positive solutions, whose energy can be made arbitrarily large. These solutions are invariant under some non-trivial sub-group of O(3) obtained doubling the equatorial. We use the finite dimensional Lyapunov–Schmidt reduction method.

AB - We consider the prescribed scalar curvature problem on SNΔSNv-N(N-2)2v+K~(y)vN+2N-2=0onSN,v>0inSN,under the assumptions that the scalar curvature K~ is rotationally symmetric, and has a positive local maximum point between the poles. We prove the existence of infinitely many non-radial positive solutions, whose energy can be made arbitrarily large. These solutions are invariant under some non-trivial sub-group of O(3) obtained doubling the equatorial. We use the finite dimensional Lyapunov–Schmidt reduction method.

KW - Finite dimensional Lyapunov–Schmidt reduction

KW - Lyapunov–Schmidt reduction

KW - Prescribed scalar curvature problem

KW - Scalar curvature problem

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DO - 10.1007/s00030-023-00845-z

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SN - 1021-9722

VL - 30

JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

IS - 3

M1 - 40

ER -

Doubling the equatorial for the prescribed scalar curvature problem on S^N

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Concentration phenomena in nonlinear analysis

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Doubling the equatorial for the prescribed scalar curvature problem on SN

Abstract

Funding

Keywords

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Concentration phenomena in nonlinear analysis

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Doubling the equatorial for the prescribed scalar curvature problem on S^N