On the dependence of the structure of boundary layers on the boundary conditions in a singularly perturbed boundary-value problem with multiple root of the related degenerate equation

We consider the two-point boundary-value problem for a singularly perturbed secondorder differential equation for the case in which the related degenerate equation has a double root. It is shown that the structure of boundary layers essentially depends on the degree of proximity of the given boundary values of the solution to the root of the degenerate equation; this phenomenon is determined by the multiplicity of the root.