论文标题
公制图上规定的质量NLS基态的独特性和非唯一性
Uniqueness and non-uniqueness of prescribed mass NLS ground states on metric graphs
论文作者
论文摘要
我们考虑了非线性schrödinger能量的规定质量基质量的唯一性问题，其功率非线性在非2CACT度量图上。我们首先确定在NLS方程中出现的Lagrange乘数在质量$μ$的基集中是恒定的，最多可计入一组质量。然后，我们将此结果应用于在两个特定的非绘制图上获得基态的唯一性。最后，我们构建了一个图表，该图至少接受具有不同lagrange乘数的相同质量的两个基态。我们的证明是基于仔细的变分论证和重排技术，并持有（2,6）$的亚临界范围$ p \，在关键情况下$ p = 6 $。
We consider the problem of uniqueness of ground states of prescribed mass for the Nonlinear Schrödinger Energy with power nonlinearity on noncompact metric graphs. We first establish that the Lagrange multiplier appearing in the NLS equation is constant on the set of ground states of mass $μ$, up to an at most countable set of masses. Then we apply this result to obtain uniqueness of ground states on two specific noncompact graphs. Finally we construct a graph that admits at least two ground states with the same mass having different Lagrange multipliers. Our proofs are based on careful variational arguments and rearrangement techniques, and hold both for the subcritical range $p\in(2,6)$ and in the critical case $p = 6$.
