  We examine global incompressible axisymmetric perturbations of a
differentially rotating MHD plasma with radial density gradients. It is shown
that the standard magnetorotational instability, (MRI) criterion drawn from the
local dispersion relation is often misleading. If the equilibrium magnetic
field is either purely axial or purely toroidal, the problem reduces to finding
the global radial eigenvalues of an effective potential. The standard Keplerian
profile including the origin is mathematically ill-posed, and thus any solution
will depend strongly on the inner boundary. We find a class of unstable modes
localized by the form of the rotation and density profiles, with reduced
dependence on boundary conditions.
