TY - CHAP
T1 - Ground State Solutions for the Nonlinear Choquard Equation with Prescribed Mass
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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U2 - 10.1007/978-3-030-73363-6_2
DO - 10.1007/978-3-030-73363-6_2
M3 - Chapter
AN - SCOPUS:85108211682
T3 - Springer INdAM Series
SP - 23
EP - 41
BT - Springer INdAM Series
PB - Springer-Verlag Italia s.r.l.
ER -