ASYMPTOTICS OF THE SOLUTION OF A SINGULARLY PERTURBED FIRST ORDER LINEAR DIFFERENTIAL EQUATION

Abstract

In this paper, we consider a singularly perturbed linear equation. In all works devoted to the study of equations where the stability condition is violated, the case is considered when there are branches (intersecting) level lines connecting the ends of the segment. In these cases, it was not necessary to consider an infinite region. Level lines connecting the ends of the segments under consideration intersect at an infinitely distant point, which is a pass point of infinite order. To obtain an asymptotic estimate near at the right ends of the segment, one has to consider an infinite domain. The problem is reduced to an integral equation and solved using the method of successive approximations.