Construction of exact solutions to singular perturbation problems for linear ordinary differential equations with power boundary layer

摘要

In contrast to earlier well-known results (see [1–4]), we show that an exact solution of the Cauchy problem with power boundary layer can be constructed in a quasiregular form convenient for a subsequent analysis, because the singularity of the solution defining the structure of the boundarylayer can be written in closed analytic form, while the other components of the solution depend on a small parameter in a regular way.