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- ItemOn a singularly perturbed initial value problem in case of a double root of the degenerate equation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 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.