Асимптотика решений однородного бисингулярно возмущенного дифференциального уравнения в теории обобщенных функций

Abstract

In the space of generalized functions, a homogeneous system of singularly perturbed differential equations in the case of stability change is considered. A theorem on generalized solutions of the corresponding degenerate system of the equation is proved. At special points, the asymptotic closeness of the solutions of the perturbed and unperturbed problems in the singular domain is established. The novelty of the work lies in the fact that, for the first time, an estimate for the singular region was obtained. A degenerate system has a special point. At this point, we solve the equation in generalized functions. In turn, this is also a novelty, because previously performed works only considered the classical solution. The following novelty of the work lies in the fact that we take the starting point in an unstable interval and also head towards the unstable interval. This property is not characteristic of previously published works.