Uniform Approximation of the Solution to a Singularly Perturbed Problem in a Particularly Critical Case

In the work, the zeros of the eigenvalues ​​of the matrix lie in the real axis. In the complex plane, we define the area in which the research is being carried out. In the case of a change in stability, at a point the level lines degenerate, and the region is divided into four parts. From the parts that correspond to the unstable segment, we select integration paths. Methods of integration paths that were previously used here are not suitable. Therefore, we are developing a new method. As a result, we obtain an estimate for the solution of the singularly perturbed problem.