Behavior of a System of Singularly Perturbed Differential Equations with Generalized Inhomogeneous Parts

The work studies systems of singularly perturbed second-order differential equations. Heterogeneity is a singular generalized Dirac function that has only a value at one point. In this case, the phenomenon of prolonged loss of stability takes place, and the estimate of solutions to the singularly perturbed problem depends on the point a.