On a singularly perturbed initial value problem in case of a double root of the degenerate equation
- Butuzov, Valentin F.
- Nefedov, Nikolai N.
- Recke, Lutz
- Schneider, Klaus
2010 Mathematics Subject Classification
- 34A12 34E05 34E15
- singularly perturbed first order ordinary differential equation, initial value problem, boundary layer, double root of degenerate equation, asymptotic expansion
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.