This note studies the asymptotic behavior of global solutions to the fourth-order Schrödinger equation

$$\begin{aligned} i\dot{u}+\Delta ^2 u+F(x,u)=0 . \end{aligned}$$

Indeed, for both cases, local and non-local source term, the scattering is obtained in the focusing mass super-critical and energy sub-critical regimes, with radial setting. This work uses a new approach due to Dodson and Murphy (Proc Am Math Soc 145(11):4859–4867, 2017).

中文翻译：

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径向聚焦非均匀双调和Schrödinger方程的能量散射

本笔记研究四阶Schrödinger方程的整体解的渐近行为

$$ \ begin {aligned} i \ dot {u} + \ Delta ^ 2 u + F（x，u）= 0。\ end {aligned} $$

确实，对于两种情况，局部和非局部源项，在径向设置的情况下，都在聚焦质量超临界和能量次临界状态下获得了散射。由于Dodson和Murphy（Proc Am Math Soc 145（11）：4859-4867，2017），这项工作使用了一种新方法。