CONSTRUCTION OF SOLUTIONS WITH EXACTLY K-BLOW-UP POINTS FOR THE SCHRODINGER-EQUATION WITH CRITICAL NONLINEARITY

We consider the nonlinear Schrödinger equation: {Mathematical expression} where u:[0, T)×ℝN→ℂ. For any given points x1, x2,..., xk in ℝN, we construct a solution of Eq. (1), u(t), which blows up in a finite time T at exactly x1, x2,..., xk. In addition, we describe the precise behavior of the solution u(t) when t→T, at the blow-up points {x1, x2,..., xk} and in ℝN-{x1, x2,..., xk}. © 1990 Springer-Verlag.