  In this paper, we consider the well-posedness of the inhomogeneous nonlinear
biharmonic Schr\"odinger equation
  with spatial inhomogeneity coefficient $K(x)$ behaves like
$\left|x\right|^{-b}$ for $0<b<\min \left\{\frac{N}{2},4\right\} $. We show the
local well-posedness in the whole $H^s$-subcritical case, with $0<s\le2$. The
difficulties of this problem come from the singularity of $K(x)$ and the lack
of differentiability of the nonlinear term. To resolve this, we derive the
bilinear Strichartz's type estimates for the nonlinear biharmonic Schr\"odinger
equations in Besov spaces.
