Influence of the Dirac function on loss progression stability of solutions to a singularly perturbed problem

The inhomogeneous part of the singularly perturbed problem affects and prolongs the loss of stability. If the inhomogeneous part is a generalized singular Dirac function, which determines the behavior of solutions to the singular problem. The features of the problem under study are shown. As a result, an asymptotic estimate was obtained. The problem is studied in a real domain.