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

Norihisa Ikoma, Yasuhito Miyamoto

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Article number2150103
JournalCommunications in Contemporary Mathematics
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • interaction estimates
  • Minimizing problem
  • nonlinear Schrödinger system
  • the multiple L 2 -constraints

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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