SEGREGATED VECTOR SOLUTIONS FOR NONLINEAR SCHRODINGER SYSTEMS IN R2

We study the following nonlinear Schrodinger system {-Delta u + P(vertical bar X vertical bar)u = mu u(3) + beta v(2)u, x is an element of R-2, -Delta v + Q(vertical bar X vertical bar)v = nu v(3) + beta u(2)v, x is an element of R-2, where P(r) and Q(r) are positive radial functions, mu > 0, nu > 0, and beta is an element of 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 non-radial positive vector solutions of segregated type when beta 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).