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We consider the inhomogeneous biharmonic nonlinear Schr\"odinger equation(IBNLS) $$ i u_t +\Delta^2 u+\lambda|x|^{-b}|u|^\alpha u = 0, $$ where$\lambda=\pm 1$ and $\alpha$, $b>0$. We show local and global well-posedness in$H^s(\mathbb{R}^N)$ in the $H^s$-subcritical case, with $s=0,2$. Moreover, weprove a stability result in $H^2(\mathbb{R}^N)$, in the mass-supercritical andenergy-subcritical case. The fundamental tools to prove these results are thestandard Strichartz estimates related to the linear problem.

On the inhomogeneous biharmonic nonlinear Schr\"odinger equation: local, global and stability results