Energy scattering for radial focusing inhomogeneous bi-harmonic Schrödinger equations

Abstract

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).