  We study boson shells and boson stars in a theory of complex scalar field
coupled to the $U(1)$ gauge field $A_{\mu}$ and Einstein gravity with the
potential: $V(|\Phi|) := \frac{1}{2} m^{2} \left(|\Phi|+ a \right)^2$. This
could be considered either as a theory of massive complex scalar field coupled
to electromagnetic field and gravity in a conical potential or as a theory in
the presence of a potential which is an overlap of a parabolic and a conical
potential. Our theory has a positive cosmological constant $(\Lambda := 4 \pi G
m^2 a^2)$. Boson stars are found to come in two types, having either ball-like
or shell-like charge density. We have studied the properties of these solutions
and have also determined their domains of existence for some specific values of
the parameters of the theory. Similar solutions have also been obtained by
Kleihaus, Kunz, Laemmerzahl and List, in a V-shaped scalar potential.
