Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation

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

*この研究の対応する著者

研究成果: Article査読

1 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)4017-4056
ページ数40
ジャーナルNonlinearity
34
6
DOI
出版ステータスPublished - 2021 6

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学
  • 物理学および天文学(全般)
  • 応用数学

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