Blow-up behavior of ground states for a nonlinear Schrödinger system with attractive and repulsive interactions

We consider a nonlinear Schrödinger system arising in a two-component Bose-Einstein condensate (BEC) with attractive intraspecies interactions and repulsive interspecies interactions in R2. We get ground states of this system by solving a constrained minimization problem. For some kinds of trapping potentials, we prove that the minimization problem has a minimizer if and only if the attractive interaction strength ai(i=1,2) of each component of the BEC system is strictly less than a threshold a⁎. Furthermore, as (a1,a2)↗(a⁎,a⁎), the asymptotical behavior for the minimizers of the minimization problem is discussed. Our results show that each component of the BEC system concentrates at a global minimum of the associated trapping potential.