Segregated vector solutions for nonlinear schrödinger systems in ℝ2

Abstract We study the following nonlinear Schrodinger system { − Δ u + P ( | x | ) u = μ u 3 + β v 2 u , x ∈ ℝ 2 , − Δ v + Q ( | x | ) v = v u 3 + β u 2 v , x ∈ ℝ 2 , where P(r) and Q(r) 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 non-radial 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).