Die Methode der Grenzschichtverbesserung für eine Masse entarteter gewöhnlicher Differentialgleichungen

Abstract

In this paper we generalize Visik’s and Ljusternik’s method for a symptotic solution of boundary value problems with a small parameter in the highest derivatives of the differential equation for a class of boundary value problems for non-self-adjoint ordinary differential equations of the order $2m$, in which the coefficients have a zero of integer order in a boundary point. A part of the arising boundary layer equations having singularities. In Chapter 3 of this paper we calculate the index of the differential operators of this boundary layer equations in a certain pair of spaces of the positive half-axis. In Chapter 4 we construct the first term of an asymptotic solition for small parameter values.