We consider the minimizing problem for the energy functional with prescribed mass constraint related to the fractional non-linear Schrödinger equation with periodic potentials. Using the concentration-compactness principle, we show a complete classification for the existence and non-existence of minimizers for the problem. In the mass-critical case, under a suitable assumption of the potential, we give a detailed description of blow-up behaviour of minimizers once the mass tends to a critical value.

中文翻译：

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具有周期势的质量临界分数非线性薛定谔方程的最小化器的存在、不存在和爆炸行为

我们考虑与具有周期性势的分数非线性薛定谔方程相关的具有规定质量约束的能量泛函的最小化问题。使用浓度紧致原则，我们对问题的最小化器的存在和不存在进行了完整的分类。在质量临界情况下，在适当的势能假设下，一旦质量趋于临界值，我们将详细描述最小化器的爆炸行为。