  In the framework of a general scalar-tensor theory, where the scalar field is
non-minimally coupled to the five-dimensional Ricci scalar curvature, we
investigate the emergence of complete brane-world solutions. By assuming a
variety of forms for the coupling function, we solve the field equations in the
bulk, and determine in an analytic way the form of the gravitational background
and scalar field in each case. The solutions are always characterized by a
regular scalar field, a finite energy-momentum tensor, and an exponentially
decaying warp factor even in the absence of a negative bulk cosmological
constant. The space-time on the brane is described by the Schwarzschild
solution leading to either a non-homogeneous black-string solution in the bulk,
when the mass parameter $M$ is non-zero, or a regular anti-de Sitter
space-time, when $M=0$. We construct physically-acceptable solutions by
demanding in addition a positive effective gravitational constant on our brane,
a positive total energy-density for our brane and the validity of the weak
energy condition in the bulk. We find that, although the theory does not allow
for all three conditions to be simultaneously satisfied, a plethora of
solutions emerge which satisfy the first two, and most fundamental, conditions.
