  In this study, we find the points of transition between elliptic and
hyperbolic regimes for the axisymmetric extended magnetohydrodynamic (MHD)
equilibrium equations. The ellipticity condition is expressed via a single
inequality but is more involved than the corresponding two-fluid ones due to
the imposition of the quasineutrality condition and is also more complicated
than the Hall MHD ellipticity condition, due to electron inertia. In fact, the
inclusion of electron inertia is responsible for peculiar results; namely, even
the static equilibrium equations can become hyperbolic.
