论文标题
半线性schrödinger方程的固定溶液，具有超临界维度的诱捕电势
Stationary solutions of semilinear Schrödinger equations with trapping potentials in supercritical dimensions
论文作者
论文摘要
通常通过使用限于能量质临界维度的变异方法来研究非线性schrödinger方程。在这里，我们基于拍摄方法介绍该方法，该方法可以在批判性和超批评性情况下提供基态存在的证明。我们为系统上的假设提出了足以使该方法起作用的假设。作为示例，我们考虑了具有谐波电位的Schrödinger-Newton和Gross-Pitaevskii方程。
Nonlinear Schrödinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach based on the shooting method that can give the proof of existence of the ground states in critical and supercritical cases. We formulate the assumptions on the system that are sufficient for this method to work. As examples, we consider Schrödinger-Newton and Gross-Pitaevskii equations with harmonic potentials.
