  The existence of envelopes is studied for systems of differential equations
in connection with the method of asymptotic splittings which allows to
determine the singularity structure of the solutions. The result is applied to
braneworlds consisting of a 3-brane in a five-dimensional bulk, in the presence
of an analog of a bulk perfect fluid parametrizing a generic class of bulk
matter. We find that all flat brane solutions suffer from a finite distance
singularity contrary to previous claims. We then study the possibility of
avoiding finite distance singularities by cutting the bulk and gluing regular
solutions at the position of the brane. Further imposing physical conditions
such as finite Planck mass on the brane and positive energy conditions on the
bulk fluid, excludes however this possibility, as well.
