The article considers the Hyers–Ulam–Rassias stability property for nonlinear systems of differential equations with a generalized effect 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. The 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 effect on the right-hand side.
Keywords: Hyers–Ulam–Rassias stability, generalized action, differential equations, discontinuous trajectories
Received February 10, 2025
Revised April 7, 2025
Accepted April 14, 2025
Alexander Nikolaevuch Sesekin, Dr. Phys.-Math. Sci., Prof., Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia; Ural Federal University, Yekaterinburg, 620000 Russia, e-mail: a.n.sesekin@urfu.ru
Anna Dmitrievna Kandrina, Ural Federal University, Yekaterinburg, 620000 Russia, e-mail: anna-kandrina@mail.ru
Nadezda Viktorovna Gredasova, Cand. Sci. (Phys-Math), Ural Federal University, Yekaterinburg, 620000 Russia, e-mail: gredasovan@mail.ru
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https://doi.org/10.1007/978-94-015-8893-5
Cite this article as: A.N. Sesekin, A.D. Kandrina, N.V. Gredasova. On the Hyers–Ulam–Rassias stability of nonlinear differential equations containing products of discontinuous and generalized functions and delays. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2025, vol 31, no. 2, pp. 205–214.
