We consider a class of L²‐supercritical inhomogeneous nonlinear Schrödinger equations with potential in three dimensions. In the focusing case, using a recent method of Dodson and Murphy, we first study the energy scattering below the ground state for the equation with radially symmetric initial data. We then establish blow‐up criteria for non‐radial solutions to the equation. In the defocusing case, we also prove the energy scattering for the equation with radially symmetric initial data.

中文翻译：

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一类带势的非齐次非线性Schrödinger方程的整体动力学

我们考虑一类具有3维势能的L ^2-超临界非均质非线性Schrödinger方程。在聚焦情况下，我们使用Dodson和Murphy的最新方法，首先研究了具有径向对称初始数据的方程在基态下的能量散射。然后，我们为方程的非径向解建立爆破准则。在散焦情况下，我们还利用径向对称的初始数据证明了方程的能量散射。