Abstract
This note studies the asymptotic behavior of global solutions to the fourth-order Schrödinger equation
i
u
˙
+
Δ
2
u
+
F
(
x
,
u
)
=
0
.
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).