On the Asymptotics of a Solution to an Elliptic Equation with a Small Parameter in a Neighborhood of an Inflection Point

Abstract

We study the asymptotic behavior of the first boundary value problem for a secondorder elliptic equation in the case where the small parameter is a factor at only one of the higher derivatives and the limit equation is an ordinary differential equation. Although the limit equation is of the same order as the original one, the problem under consideration is bisingular. We investigate the asymptotic behavior of this problem using the method of matched asymptotic expansions.