On One Singularly Perturbed System of Ordinary Differential Equations with Multiple Root of the Degenerate Equation

Abstract

We consider a boundary-value problem for a system of two ordinary differential equations of the second order with different powers of the small parameter as coefficients of the second derivatives in both equations. One equation of the degenerate system possesses a double root. This leads to qualitative differences between the asymptotics of the boundary-layer solution of the analyzed system and the known asymptotics in the case of simple roots of the equations of degenerate system, namely, the structure of the boundary-layer series changes, the boundary layers are multizone, and the standard algorithm used for the construction boundary-layer functions becomes inapplicable and requires significant modifications.