This paper studies the mass-critical variable coefficient nonlinear Schrödinger equation. We first get the existence of the ground state by solving a minimization problem. Then we prove a compactness result by the variational characterization of the ground state solutions. In addition, we construct the blow-up solutions at the minimal mass threshold and further prove the uniqueness result on the minimal mass blow-up solutions which are pseudo-conformal transformation of the ground states.

中文翻译：

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变势非线性薛定谔方程的最小质量爆破解

本文研究了质量临界变系数非线性薛定谔方程。我们首先通过解决最小化问题来获得基态的存在。然后我们通过基态解的变分表征证明了紧凑性结果。此外，我们构造了最小质量阈值下的爆破解，并进一步证明了作为基态伪共形变换的最小质量爆破解的唯一性结果。