论文标题
评论具有谐波潜力的分数NLS基态解决方案的独特性
Comment on the Uniqueness of the Ground State Solutions of a Fractional NLS with a Harmonic Potential
论文作者
论文摘要
[1，2]中开发的突破方法尚未涵盖具有谐波电位的分数浮动方程的阳性基态解决方案的独特性。多年来，它一直是一个悬而未决的问题。 [3]和[5]最近能够证明基态解决方案的存在并获得重要特性，但他们未能解决独特性。 [3]将其作为一个空旷的问题，[5]运行有利于独特性的数值模拟。最近，本说明的作者开发了一种通用和统一的方法，以证明大量变分问题的基态解决方案的独特性，他们还展示了许多适用其方法的例子。 [4]发表后，一些同事与我们联系，知道我们的方法是否适用于具有谐波潜力的分数shrodinger方程。在简短的说明中，我们将解释它的应用方式，我们还将陈述归一化的某些存在/不存在和多样性解决方案
The uniqueness of the positive ground state solutions of fractional Shrodinger equations with a harmonic potential has not been covered by the breakthrough method developed in [1, 2]. It has remained an open question for years. [3] and [5] were quite recently able to prove the existence of the ground state solutions and to derive important properties but they failed to address the uniqueness. [3] left it as an open question, and [5] run numerical simulations that were in favor of the uniqueness. Very recently, the authors of this note developed a general and unified method to prove the uniqueness of the ground state solutions of a large class of variational problems, they also exhibited many examples to which their approach applies. After the publication of [4], some colleagues reached out to us to know whether our method applies to the fractional Shrodinger equation with a harmonic potential. In this short note, we will explain how it applies, and we will also state some existence/ non-existence and multiplicity solutions of the normalized
