Yujin Guo, Robert Seiringer
We consider two-dimensional Bose-Einstein condensates with attractive interaction, described by the Gross-Pitaevskii functional. We prove that minimizers exist if and 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.
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http://arxiv.org/abs/1301.5682
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