Nondegeneracy of nodal solutions to the critical Yamabe problem

Monica Musso, Juncheng Wei

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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.
Original languageEnglish
Pages (from-to)1049-1107
Number of pages59
JournalCommunications in Mathematical Physics
Volume340
Issue number3
Early online date24 Sep 2015
DOIs
Publication statusPublished - 1 Dec 2015

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