  We analyze combined effects of the geometry produced by global monopole and a
concentric spherical boundary on the self-energy of a point-like scalar charged
test particle at rest. We assume that the boundary is outside the monopole's
core with a general spherically symmetric inner structure. An important
quantity to this analysis is the three-dimensional Green function associated
with this system. For both Dirichlet and Neumann boundary conditions obeyed by
the scalar field on the sphere, the Green function presents a structure that
contains contributions due to the background geometry of the spacetime and the
boundary. Consequently the corresponding induced scalar self-energy present
also similar structure. For points near the sphere the boundary-induced part
dominates and the self-force is repulsive/attractive with respect to the
boundary for Dirichlet/Neumann boundary condition. In the region outside the
sphere at large distances from it, the boundary-free part in the self-energy
dominates and the corresponding self-force can be either attractive or
repulsive with dependence of the curvature coupling parameter for scalar field.
In particular, for the minimal coupling we show the presence of a stable
equilibrium point for Dirichlet boundary condition. In the region inside the
sphere the nature of the self-force depends on the specific model for the
monopole's core. As illustrations of the general procedure adopted we shall
consider two distinct models, namely flower-pot and the ballpoint-pen ones.
