论文标题
能量超临界毛皮的基础状态，具有谐波电势
Ground state in the energy super-critical Gross-Pitaevskii equation with a harmonic potential
论文作者
论文摘要
在特定的情况下，在特定情况下，重新审视了具有谐波电位的能量超临界毛 - Pitaevskii方程，以焦点的非线性和尺寸为d> 4。我们证明，解决方案曲线（特征值参数的图与超级属性的图）对于d <= 12的振荡性是D <= 12的振荡性，而D> = 13的单调元素与现有文献相比，严格的渐近渐近学是通过用功能 - 分析的三个固定方程来构建固定方程的三个族来得出的，而不是函数分析方法。
The energy super-critical Gross--Pitaevskii equation with a harmonic potential is revisited in the particular case of cubic focusing nonlinearity and dimension d > 4. In order to prove the existence of a ground state (a positive, radially symmetric solution in the energy space), we develop the shooting method and deal with a one-parameter family of classical solutions to an initial-value problem for the stationary equation. We prove that the solution curve (the graph of the eigenvalue parameter versus the supremum) is oscillatory for d <= 12 and monotone for d >= 13. Compared to the existing literature, rigorous asymptotics are derived by constructing three families of solutions to the stationary equation with functional-analytic rather than geometric methods.
