On the inhomogeneous biharmonic nonlinear Schrödinger equation: Local, global and stability results
Abstract We consider the inhomogeneous biharmonic nonlinear Schrodinger equation (IBNLS) i u t + Δ 2 u + λ | x | − b | u | α u = 0 , where λ = ± 1 and α , b > 0 . We show local and global well-posedness in H s ( R N ) in the H s -subcritical case, with s = 0 , 2 . Moreover, we prove a stability result in H 2 ( R N ) , in the mass-supercritical and energy-subcritical case. The fundamental tools to prove these results are the standard Strichartz estimates related to the linear problem.