Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation

S. Cingolani*, M. Gallo, K. Tanaka

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


We study existence of solutions for the fractional problemwhere N 2, s ∈ (0, 1), m > 0, μ is an unknown Lagrange multiplier and satisfies Berestycki-Lions type conditions. Using a Lagrangian formulation of the problem (P m ), we prove the existence of a weak solution with prescribed mass when g has L 2 subcritical growth. The approach relies on the construction of a minimax structure, by means of a Pohozaev's mountain in a product space and some deformation arguments under a new version of the Palais-Smale condition introduced in Hirata and Tanaka (2019 Adv. Nonlinear Stud. 19 263-90); Ikoma and Tanaka (2019 Adv. Differ. Equ. 24 609-46). A multiplicity result of infinitely many normalized solutions is also obtained if g is odd.

Original languageEnglish
Pages (from-to)4017-4056
Number of pages40
Issue number6
Publication statusPublished - 2021 Jun


  • Lagrange multiplier
  • Pohozaev identity
  • nonlinear Schr dinger equation
  • normalized solution
  • prescribed massfractional Laplacian
  • radially symmetric solution

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics


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