On the Hyers–Ulam–Rassias Stability of Nonlinear Differential Equations Containing Products of Discontinuous and Generalized Functions and Delays

The article considers the Hyers–Ulam–Rassias stability property for nonlinear systems of differential equations with a generalized action on the right-hand side. Since the right-hand side of the systems under consideration is unbounded, the standard definition of the stability property under consideration cannot be used. A formalization of the Hyers–Ulam–Rassias stability concept for nonlinear systems of differential equations with delay and discontinuous trajectories is given. Sufficient conditions are obtained that ensure such stability for a nonlinear system of differential equations with delay and a generalized action on the right-hand side.