  The steady-state structure of a disc with a corona is analyzed when the
vertical component of the gravitational force due to the self-gravity of the
disc is considered. For the energy exchange between the disc and the corona, we
assume a fraction f of the dissipated energy inside the accretion disc is
transported to the corona via the magnetic tubes. Analytical solutions
corresponding to a prescription for f (in which this parameter directly depends
on the ratio of the gas pressure to the total pressure) or free f are presented
and their physical properties are studied in detail. We show that the existence
of the corona not only decreases the temperature of the disc, but also
increases the surface density.The vertical component of the gravitational force
due to the self-gravity of the disc decreases the self-gravitating radius and
the mass of the fragments at this radius. However, as more energy is
transported from the disc to the corona, the effect of the vertical component
of the gravitational force due to the self-gravity of the disc on the
self-gravitating radius becomes weaker, though the mass of the fragments is
reduced irrespective of the amount of the energy exchange from the disc to the
corona.
