SEGREGATED VECTOR SOLUTIONS FOR NONLINEAR SCHR?DINGER SYSTEMS IN R~2

We study the following nonlinear Schrodinger system where P(τ) and Q(τ) are positive radial functions,μ 0,v 0,and β∈ R is a coupling constant.This type of system arises,particularly,in models in Bose-Einstein condensates theory.Applying a finite reduction method,we construct an unbounded sequence of nonradial positive vector solutions of segregated type when β is in some suitable interval,which gives an answer to an interesting problem raised by Peng and Wang in Remark 4.1(Arch.Ration.Mech.Anal.,208(2013),305-339).