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 $$i\dot{u}+{\Delta }^{2}u+F(x,u)=0.$$ 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-Murphy \cite{dm}.

arXiv admin note: substantial text overlap with arXiv:2010.07760