Nodal solutions for the fractional Yamabe problem on Heisenberg groups

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Abstract

We prove that the fractional Yamabe equation on the Heisenberg group Hn has [n + 1/2] sequences of nodal (sign-changing) weak solutions whose elements have mutually different nodal properties, where denotes the CR fractional sub-Laplacian operator on Hn, Q = 2n + 2 is the homogeneous dimension of Hn, and. Our argument is variational, based on a Ding-type conformal pulling-back transformation of the original problem into a problem on the CR sphere S2n + 1 combined with a suitable Hebey-Vaugon-type compactness result and group-theoretical constructions for special subgroups of the unitary group U(n + 1).

Original languageEnglish
Pages (from-to)771-788
Number of pages18
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume150
Issue number2
DOIs
Publication statusPublished - Apr 1 2020

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Keywords

  • CR fractional sub-Laplacian
  • Heisenberg group
  • nodal solution

ASJC Scopus subject areas

  • Mathematics(all)

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