Expanding the Areas of Attraction of Solutions to Singularly Perturbed Equations

In this paper, a singularly perturbed equation of the first order is considered, the concept of a region of attraction (DO) of the solution of a singularly perturbed equation to the solution of an unperturbed equation is introduced, and the existence of an OA is proved. The problem has been set about the possibility of expanding the areas of attraction of VCA solutions. It has been proven that if there is a region of attraction, then it can be expanded to the boundary of the region under consideration. In the proof, geometric constructions were used, using the level line of conjugate-harmonic functions, the method of successive approximations and methods of asymptotic estimates.