### Abstract

: We prove the existence of a sequence of nondegenerate, in the sense of

Duyckaerts–Kenig–Merle [9], nodal nonradial solutions to the critical Yamabe problem−Q = |Q| 2n−2 Q, Q ∈ D1,2(Rn).

This is the first example in the literature of nondegeneracy for nodal nonradial solutions of nonlinear elliptic equations and it is also the only nontrivial example for which the result of Duyckaerts–Kenig–Merle [9] applies.

Duyckaerts–Kenig–Merle [9], nodal nonradial solutions to the critical Yamabe problem−Q = |Q| 2n−2 Q, Q ∈ D1,2(Rn).

This is the first example in the literature of nondegeneracy for nodal nonradial solutions of nonlinear elliptic equations and it is also the only nontrivial example for which the result of Duyckaerts–Kenig–Merle [9] applies.

Original language | English |
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Pages (from-to) | 1049-1107 |

Number of pages | 59 |

Journal | Communications in Mathematical Physics |

Volume | 340 |

Issue number | 3 |

Early online date | 24 Sep 2015 |

DOIs | |

Publication status | Published - 1 Dec 2015 |

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## Cite this

Musso, M., & Wei, J. (2015). Nondegeneracy of nodal solutions to the critical Yamabe problem.

*Communications in Mathematical Physics*,*340*(3), 1049-1107. https://doi.org/10.1007/s00220-015-2462-1