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This example has demonstrated how boundary-layer techniques are equally applicable
to interior (transition) layers and, further, they need not be restricted to single layers.
Some problems exhibit multiple layers; for example

has transition layers both near x = 1/2 and near x = –1/2, and the solution away
from these layers is now in three parts.
A type of problem which contains elements of both boundary and transition layers
occurs if the coefficient, a(x), of is zero at one (or both) boundaries. Because
at an internal point, it is not a transition layer, but the fact that at
the end-point affects the scaling—it is no longer in general—and this must be
determined directly (as we did for the transition layer).

E2.16 A boundary-layer problem with a new scaling
We consider the equation

for with and note that and so we must
expect a boundary layer near x = 0. Away from x = 0, we seek a solution

which gives

and so on, with and for Thus we obtain

in order to satisfy the boundary condition (and as this does not approach
and so a boundary layer is certainly required). The equation for is
therefore

or