  The existence of a simple spherically symmetric and static solution of the
Einstein equations in the presence of a cosmological constant vanishing outside
a definite value of the radial distance is investigated. A particular
succession of field configurations, which are solutions of the Einstein
equations in the presence of the considered cosmological term and auxiliary
external sources, is constructed. Then, it is shown that the associated
succession of external sources tend to zero in the sense of the generalized
functions. The type of weak solution that is found becomes the deSitter
homogeneous space-time for the interior region, and the Schwartzschild space in
the outside zone.
