Construction of solutions with exactly k blow-up points for nonlinear Schrödinger equation with a harmonic potential

摘要

In this paper we consider the nonlinear Schrödinger equation with a harmonic potential, which describes Bose–Einstein condensate. For arbitrarily given k points x1,x2,…,xk in Rn, we construct a solution which blows up exactly at x1,x2,…,xk. Furthermore, the precise behavior of the solution is described both at those blow-up points and in ⧹Rn⧹{x1,x2,…,xk}.