  We derive the full projected Einstein-Brans-Dicke gravitational equations
associated with a n-dimensional brane embedded in a (n+1)-dimensional bulk. By
making use of general conditions, as the positivity of the Brans-Dicke
parameter and the effective Newton gravitational constant as well, we are able
to constrain the brane cosmological constant in terms of the brane tension, the
Brans-Dicke scalar field, and the trace of the stress tensor on the brane, in
order to achieve a $dS$ brane. Applying these constraints to a specific
five-dimensional model, a lower bound for the scalar field on the brane is
elicited without solving the full equations. It is shown under which conditions
the brane effective cosmological constant can be ignored in the brane projected
gravitational field equations, suggesting a different fine tuning between the
brane tension and the bulk cosmological.
