Singularly Perturbed Boundary Value Problem with Multizonal Interior Transitional Layer

Abstract

Two-point boundary value problem for a singularly perturbed ordinary differential equation of second order is considered in the case when the degenerate equation has three unintersecting roots from which one root is two-tuple and two roots are one-tuple. It is prooved that for sufficiently small values of the small parameter the problem has a solution with the transition from the two-tuple root of the degenerate equation to the one-tuple root in the neighbourhood of an internal point of the interval. The asymptotic expansion of this solution is constructed. It distinguishes from the known expansion in the case when all roots of the degenerate equation are one-tuple, in particular, the transitional layer is multizonal.

Keywords

• сингулярно возмущённое уравнение
• внутренний переходный слой
• асимптотическое разложение решения