论文标题
一种新方法，证明NLS的存在，不存在，多样性，独特性和轨道稳定性/轨道稳定性/轨道稳定性/不稳定性
A New Method to prove the Existence, Non-existence, Multiplicity, Uniqueness, and Orbital Stability/Instability of standing waves for NLS with partial confinement
论文作者
论文摘要
我们提供了一种新方法，以证明NLS的存在，不存在，多样性，轨道稳定性/轨道稳定性/不稳定性，即使在还原方程中，也没有次临界假设。使用这种方法，我们为[7，备注1.10]提出的一个开放问题给出了肯定的答案，其中作者猜想的存在不仅仅是归一化解决方案。我们还根据分叉参数确定基态解决方案的唯一性结果。我们解释说，当部分限制的效果很强时，某些参数会降低维度。我们还发现从完全限制的案件中发现了不同的分叉现象。
We give a new method to prove the existence, non-existence, multiplicity, orbital stability/instability of standing waves for NLS with partial confinement without the subcritical hypothesis, even in the reduction equation. Using this method, we give an affirmative answer for an open problem proposed by [7, Remark 1.10] where the authors conjectured the existence of more than a normalized solution. We also establish uniqueness results of the ground state solutions depending on the bifurcation parameters. We explain that when the effect of partial confinement is strong, a dimension reduction appears for some parameters. We also find different bifurcation phenomena from the cases with full confinement.
