Singularly perturbed boundary value problem with multizonal interior transitional layer

The paper discusses a two-point boundary value problem for a singularly perturbed ordinary second-order differential equation in the case when the degenerate equation has three nonintersecting roots from which one root is twofold and two roots are onefold. It is proved that the problem has a solution with transition from the twofold root of the degenerate equation to the onefold root in the neighborhood of a point of the interval for sufficiently small parameter values. An asymptotic expansion of this solution is constructed. It is distinguished from the known expansion when all the roots of the degenerate equation are onefold; in particular, the transitional layer is multizonal.