A note on the fourth-order Schrodinger equation with spatially growing inhomogeneous source term
Analysis of PDEs
2026-05-12 v2
Abstract
This paper studies a non-linear biharmonic Sch\"odinger equation with an unbounded inhomogeneous term. The main goal is to develop a local theory but also a global theory for small data, in the energy space. Moreover, we develop a local theory in Sobolev spaces with lower regularity. The challenge is to deal with the inhomogeneous unbounded term, which broke down the space translation invariance. In order to handle the inhomogenous term, we use some Strauss type estimates, which require a spherically symmetric assumption.
Keywords
Cite
@article{arxiv.2511.06985,
title = {A note on the fourth-order Schrodinger equation with spatially growing inhomogeneous source term},
author = {Alaa Mohammed Alqaied and Tarek Saanouni},
journal= {arXiv preprint arXiv:2511.06985},
year = {2026}
}