论文标题
等效于基态以下的初始数据与具有排斥力电势的NLS
Equivalence of conditions on initial data below the ground state to NLS with a repulsive inverse power potential
论文作者
论文摘要
在本文中，我们考虑了具有排斥力电位的非线性schrödinger方程。首先，我们表明，一些全球范围良好的结果和“爆炸或成长”结果低于基态，而没有潜力。然后，我们证明条件在基础状态以下的初始数据上等效。我们注意到，最近，我们建立了径向基态的存在，并通过[8]中两个或更高空间维度的NLS的病毒功能来表征它。然后，我们还证明了全球适应性良好的结果，并且在[8]中获得的排斥反向功率电位低于径向基态下的“爆炸或成长”结果。
In this paper, we consider the nonlinear Schrödinger equation with a repulsive inverse power potential. First, we show that some global well-posedness results and "blow-up or grow-up" results below the ground state without the potential. Then, we prove equivalence of the conditions on the initial data below the ground state without potential. We note that recently, we established existence of a radial ground state and characterized it by the virial functional for NLS with a general potential in two or higher space dimensions in [8]. Then, we also prove a global well-posedness result and a "blow-up or grow-up" result below the radial ground state with a repulsive inverse power potential obtained in [8].
