Ground States for a Nonlinear Schrödinger System with Sublinear Coupling Terms

Filipe Oliveira, Hugo Tavares

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We study the existence of ground states for the coupled Schrödinger system -Δu i +λ i u i =μ i |u i | 2q-2 u i +j i b ij |u j | q |u i | q-2 u i ,u i H 1 (n ),i=1,...,d,$ -\Delta u-i+\lambda -i u-i= \mu -i |u-i|{2q-2}u-i+\sum -{j\ne i}b-{ij} |u-j|q|u-i|{q-2}u-i, \quad u-i\in H1(\mathbb {R}n), \quad i=1,\ldots , d, $ n ≥ 1, for λ i ,μ i >0${\lambda -i,\mu -i >0}$ , b ij =b ji >0${b-{ij}=b-{ji}>0}$ (the so-called "symmetric attractive case") and 1i radially decreasing. Moreover, we show that if in addition q

Original languageEnglish
Pages (from-to)381-387
Number of pages7
JournalAdvanced Nonlinear Studies
Volume16
Issue number2
DOIs
Publication statusPublished - 1 May 2016

Keywords

  • Coupled Nonlinear Schrödinger Systems
  • Nehari Manifold
  • Nontrivial Ground States

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