Some remarks on the inhomogeneous biharmonic NLS equation

We consider the inhomogeneous biharmonic nonlinear Schrödinger equation iut+?2u+?|x|?b|u|?u=0,where ?=±1 and ?, b>0. In subctritical case, we improve global well-posedness result obtained in Guzmán Pastor (2020) for dimensions N=5,6,7 Sobolev space H2(RN). The fundamental tools to establish our results are standard Strichartz estimates related linear problem Hardy-Littlewood inequality. Results concerning energy-critical that is, ?=8?2bN?4 also reported. More precisely, show a stability with initial data critical H?2.