  We study fully localized BPS brane solutions in classical supergravity using
a perturbative approach to the coupled Born-Infeld/bulk supergravity system. We
derive first order bulk supergravity fields for world-volume solitons
corresponding to intersecting M2-branes and to a fundamental string ending on a
D3-brane. One interesting feature is the appearance of certain off-diagonal
metric components and corresponding components of the gauge potentials. Making
use of a supersymmetric ansatz for the exact fields, we formulate a
perturbative expansion which applies to $M2 \perp M2 (0), M5 \perp M5 (3)$ and
$Dp \perp Dp (p-2)$ intersections. We find that perturbation theory
qualitatively distinguishes between certain of these cases: perturbation theory
breaks down at second order for intersecting M2-branes and D$p$-branes with
$p\le 3$ while it is well behaved, at least to this order, for the remaining
cases. This indicates that the behavior of the full non-linear intersecting
Dp-brane solutions may be qualitatively different for $p \le 3$ than for $p \ge
4$, and that fully localized asymptotically flat solutions for $p \le 3$ may
not exist. We discuss the consistency of these results with world-volume field
theory properties.
