  We consider two-dimensional Bose-Einstein condensates with attractive
interaction, described by the Gross-Pitaevskii functional. Minimizers of this
functional exist only if the interaction strength $a$ satisfies $a < a^*=
\|Q\|_2^2$, where $Q$ is the unique positive radial solution of $\Delta
u-u+u^3=0$ in $\R^2$. We present a detailed analysis of the behavior of
minimizers as $a$ approaches $a^*$, where all the mass concentrates at a global
minimum of the trapping potential.
