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

Norihisa Ikoma, Yasuhito Miyamoto

研究成果: Article査読

5 被引用数 (Scopus)

抄録

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.

本文言語English
論文番号2150103
ジャーナルCommunications in Contemporary Mathematics
25
2
DOI
出版ステータスPublished - 2023 3月 1

ASJC Scopus subject areas

  • 数学一般
  • 応用数学

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