TY - JOUR
T1 - Multiplicity of Normalized Solutions to a Class of Non-autonomous Choquard Equations
AU - Meng, Yuxi
AU - Wang, Bo
N1 - Publisher Copyright:
© Mathematica Josephina, Inc. 2024.
PY - 2025/1
Y1 - 2025/1
N2 - In this paper, we consider the multiplicity of solutions to the following Choquard equation (Formula presented.) with a prescribed mass (Formula presented.) where N≥1, a,ε>0, α∈(0,N), N+αNα is the Riesz potential, λ∈R appears as an unknown Lagrange multiplier, h:RN→[0,∞) is a bounded and continuous function and the potential V is a continuous function. Under some assumptions on V, we show that when ε is small enough the numbers of normalized ground states are at least the numbers of global maximum points of h.
AB - In this paper, we consider the multiplicity of solutions to the following Choquard equation (Formula presented.) with a prescribed mass (Formula presented.) where N≥1, a,ε>0, α∈(0,N), N+αNα is the Riesz potential, λ∈R appears as an unknown Lagrange multiplier, h:RN→[0,∞) is a bounded and continuous function and the potential V is a continuous function. Under some assumptions on V, we show that when ε is small enough the numbers of normalized ground states are at least the numbers of global maximum points of h.
KW - 35A15
KW - 35J15
KW - Choquard equations
KW - Multiplicity
KW - Normalized solutions
KW - Variational method
UR - http://www.scopus.com/inward/record.url?scp=85208734650&partnerID=8YFLogxK
U2 - 10.1007/s12220-024-01844-x
DO - 10.1007/s12220-024-01844-x
M3 - Article
AN - SCOPUS:85208734650
SN - 1050-6926
VL - 35
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 1
M1 - 12
ER -