  The stability of the recently proposed static solutions for boson stars is
analyzed. These solutions of Einstein-Klein-Gordon (EKG) equations arise from
considering the interaction of a real scalar field with matter. We assume that
the inclusion of the scalar field in addition with matter, allows to justify
that stability implies that the total mass of the solution should grow when the
initial condition for the density of matter at the origin is also increased.
Employing numerical values for the static boson star based on a linear relation
between the source and the energy density and between this and the pressure, we
found the relation that linked the the scalar field at the origin with the
matter energy density (MED) in the same point. We also determine the behavior
of the total mass (TM) with the matter energy density in the origin, by also
obtaining through this and the weak energy condition, two possible ranges for
stable solutions of static boson stars.
