Ground State Solutions for the Nonlinear Choquard Equation with Prescribed Mass

Silvia Cingolani; Kazunaga Tanaka

doi:10.1007/978-3-030-73363-6_2

Ground State Solutions for the Nonlinear Choquard Equation with Prescribed Mass

Silvia Cingolani^*, Kazunaga Tanaka

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Chapter

10 Citations (Scopus)

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 language	English
Title of host publication	Springer INdAM Series
Publisher	Springer-Verlag Italia s.r.l.
Pages	23-41
Number of pages	19
DOIs	https://doi.org/10.1007/978-3-030-73363-6_2
Publication status	Published - 2021

Publication series

Name	Springer INdAM Series
Volume	47
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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10.1007/978-3-030-73363-6_2

Cite this

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title = "Ground State Solutions for the Nonlinear Choquard Equation with Prescribed Mass",

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.",

keywords = "Lagrange formulation, Nonlinear Choquard equation, Nonlocal nonlinearities, Normalized solutions, Positive solutions",

author = "Silvia Cingolani and Kazunaga Tanaka",

note = "Funding Information: The second author supported in part by Grant-in-Aid for Scientific Research (JP19H00644, JP18KK0073, JP17H02855, JP16K13771, JP26247014) of Japan Society for the Promotion of Science. Funding Information: The first author is supported by PRIN 2017JPCAPN “Qualitative and quantitative aspects of nonlinear PDEs” and by INdAM-GNAMPA. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2021",

doi = "10.1007/978-3-030-73363-6_2",

language = "English",

series = "Springer INdAM Series",

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AU - Cingolani, Silvia

AU - Tanaka, Kazunaga

N1 - Funding Information: The second author supported in part by Grant-in-Aid for Scientific Research (JP19H00644, JP18KK0073, JP17H02855, JP16K13771, JP26247014) of Japan Society for the Promotion of Science. Funding Information: The first author is supported by PRIN 2017JPCAPN “Qualitative and quantitative aspects of nonlinear PDEs” and by INdAM-GNAMPA. Publisher Copyright: © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Lagrange formulation

KW - Nonlinear Choquard equation

KW - Nonlocal nonlinearities

KW - Normalized solutions

KW - Positive solutions

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SP - 23

EP - 41

BT - Springer INdAM Series

PB - Springer-Verlag Italia s.r.l.

ER -

Ground State Solutions for the Nonlinear Choquard Equation with Prescribed Mass

Abstract

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Keywords

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