2012, Butuzov, Valentin F., Nefedov, Nikolai N., Recke, Lutz, Schneider, Klaus R.

We study the initial value problem of a singularly perturbed first order ordinary differential equation in case that the degenerate equation has a double root. We construct the formal asymptotic expansion of the solution such that the boundary layer functions decay exponentially. This requires a modification of the standard procedure. The asymptotic solution will be used to construct lower and upper solutions guaranteeing the existence of a unique solution and justifying its asymptotic expansion.