Ground State Solutions for the Nonlinear Choquard Equation with Prescribed Mass

Silvia Cingolani, Kazunaga Tanaka

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We study existence of radially symmetric solutions for the nonlocal problem: where (formula presetned) a unknown Lagrange multiplier. Using a Lagrange formulation of the problem (1 ), we develop new deformation arguments under a version of the Palais-Smale condition introduced in the recent papers (Hirata and Tanaka, Adv Nonlinear Stud 19:263–290, 2019; Ikoma and Tanaka, Adv Differ Equ 24:609–646, 2019) and we prove the existence of a ground state solution for the nonlinear Choquard equation with prescribed mass, when F satisfies Berestycki-Lions type conditions.

Original languageEnglish
Title of host publicationSpringer INdAM Series
PublisherSpringer-Verlag Italia s.r.l.
Pages23-41
Number of pages19
DOIs
Publication statusPublished - 2021

Publication series

NameSpringer INdAM Series
Volume47
ISSN (Print)2281-518X
ISSN (Electronic)2281-5198

Keywords

  • Lagrange formulation
  • Nonlinear Choquard equation
  • Nonlocal nonlinearities
  • Normalized solutions
  • Positive solutions

ASJC Scopus subject areas

  • Mathematics(all)

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