Hartree问题谱稳定驻波的分类
On the classification of the spectrally stable standing waves of the Hartree problem
摘要：
考虑了具有一般幂非线性和空间维数的分数阶Hartree模型。我们构造变分的“规范化”的解决方案，相应的Choquard-Pekar模型-特别是一些关键的属性，如光滑性和钟形的建立。作为一个后果的建设，我们表明，这些孤子是光谱稳定的时间相关的Hartree模型的解决方案。此外，我们分析了经典Hartree问题的Moroz-Van Schaftingen孤子在任意维数和幂次非线性下的谱稳定性。一个完整的分类，其中的主要结论是，只有和确切的“正规化”的解决方案（只存在于一部分的范围）是谱稳定的。
英文摘要：
We consider the fractional Hartree model, with general power non-linearity and space dimension. We construct variationally the "normalized" solutions for the corresponding Choquard-Pekar model - in particular a number of key properties, like smoothness and bell-shapedness are established. As a consequence of the construction, we show that these solitons are spectrally stable as solutions to the time-dependent Hartree model. In addition, we analyze the spectral stability of the Moroz-Van Schaftingen solitons of the classical Hartree problem, in any dimensions and power non-linearity. A full classification is obtained, the main conclusion of which is that only and exactly the "normalized" solutions (which exist only in a portion of the range) are spectrally stable.
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