TY - JOUR

T1 - The compactness of minimizing sequences for a nonlinear Schrödinger system with potentials

AU - Ikoma, Norihisa

AU - Miyamoto, Yasuhito

N1 - Publisher Copyright:
© 2023 World Scientific Publishing Company.

PY - 2023/3/1

Y1 - 2023/3/1

N2 - In this paper, we consider the following minimizing problem with two constraints: inf E(u)|u = (u1,u2),u1L22 = α 1,u2L22 = α 2, where α1,α2 > 0 and E(u) is defined by E(u):= N 1 2i=12(|u i|2 + V i(x)|ui|2) - i=12 μi 2pi + 2|ui|2pi+2 - β p3 + 1|u1|p3+1|u 2|p3+1 dx. Here N ≥ 1, μ1,μ2,β > 0 and Vi(x) (i = 1, 2) are given functions. For Vi(x), we consider two cases: (i) both of V1 and V2 are bounded, (ii) one of V1 and V2 is bounded. Under some assumptions on Vi and pj, we discuss the compactness of any minimizing sequence.

AB - In this paper, we consider the following minimizing problem with two constraints: inf E(u)|u = (u1,u2),u1L22 = α 1,u2L22 = α 2, where α1,α2 > 0 and E(u) is defined by E(u):= N 1 2i=12(|u i|2 + V i(x)|ui|2) - i=12 μi 2pi + 2|ui|2pi+2 - β p3 + 1|u1|p3+1|u 2|p3+1 dx. Here N ≥ 1, μ1,μ2,β > 0 and Vi(x) (i = 1, 2) are given functions. For Vi(x), we consider two cases: (i) both of V1 and V2 are bounded, (ii) one of V1 and V2 is bounded. Under some assumptions on Vi and pj, we discuss the compactness of any minimizing sequence.

KW - Minimizing problem

KW - interaction estimates

KW - nonlinear Schrödinger system

KW - the multiple L 2 -constraints

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U2 - 10.1142/S0219199721501030

DO - 10.1142/S0219199721501030

M3 - Article

AN - SCOPUS:85121681068

SN - 0219-1997

VL - 25

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

IS - 2

M1 - 2150103

ER -