  We derive a boundary layer equation describing accumulation regions within a
thin-film approximation framework where gravity and surface tension balance. As
part of the analysis of this problem we investigate in detail and rigorously
the 'drainage' equation (phi"'+1)phi^3=1. In particular, we prove that all
solutions that do not tend to 1 as the independent variable goes to infinity
are oscillatory, and that they oscillate in a very specific way. This result
and the method of proof will be used in the analysis of solutions of the afore
mentioned boundary layer problem.
