Segregated Vector Solutions For Nonlinear Schrodinger Systems In R~2

We study the following nonlinear Schrodinger systemwhere P(r)and Q(r)are positive radial functions,?>0,v>0,??R is a cou-pling 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 non-radial positive vector solutions of segregated type when ? is in some suitable interval,which gives an answer to an interesting problem raised by Peng and Wang in Remark 4.1.