Geodesic
Hyers--Ulam--Rassias stability of nonlinear differential equations with a generalized actions on the right-hand side
Ural mathematical journal, Tome 9 (2023) no. 1, pp. 147-152

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The paper considers the Hyers–Ulam–Rassias stability for systems of nonlinear differential equations with a generalized action on the right-hand side, for example, containing impulses — delta functions. The fact that the derivatives in the equation are considered distributions required a correction of the well-known Hyers–Ulam–Rassias definition of stability for such equations. Sufficient conditions are obtained that ensure the property under study.
Keywords: Hyers–Ulam–Rassias stability, differential equations, generalized actions, discontinuous trajectories. 
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     author = {Alexander N. Sesekin and Anna D. Kandrina},
     title = {Hyers--Ulam--Rassias stability of nonlinear differential equations with a generalized actions on the right-hand side},
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     url = {http://geodesic.mathdoc.fr/item/UMJ_2023_9_1_a12/}
}
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Alexander N. Sesekin; Anna D. Kandrina. Hyers--Ulam--Rassias stability of nonlinear differential equations with a generalized actions on the right-hand side. Ural mathematical journal, Tome 9 (2023) no. 1, pp. 147-152. http://geodesic.mathdoc.fr/item/UMJ_2023_9_1_a12/