Asymptotics of solutions to a singularly perturbed problem

The work examines the asymptotics of solutions to singularly perturbed differential equations. The zeros of the matrix eigenvalues lie on the real axis. Moving on to the complex plane, we define the negative region in which the research is carried out. Level lines completely cover this area. One of the level lines divides the area into four parts. In each of these parts of the region we choose integration paths. The integration paths should be as decreasing from the starting point to the last point. Carrying out calculations along the chosen integration path, we obtain asymptotic estimates for solutions of singularly perturbed differential equations.