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

Norihisa Ikoma, Yasuhito Miyamoto

研究成果: Article査読

1 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):= RN 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
DOI
出版ステータスAccepted/In press - 2021

ASJC Scopus subject areas

  • 数学 (全般)
  • 応用数学

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