Abstract
By extending the concept of normal cone for a class of not necessarily convex sets in the \(n \)-dimensional Euclidean space, we generalize the concept of system with diode nonlinearities, for which a theorem on the existence of a solution of the initial value problem is proved. An example of the problem is given that shows that the uniqueness of the solution does not hold.
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REFERENCES
Appell, J., Nguyen Thi Hien, Petrova, L., and Pryadko, I., Systems with Non-Smooth Inputs, Berlin–Boston: De Gruyter, 2021.
Lobanova, O.A. and Sadovskii, B.N., On two-dimensional dynamical systems with a constraint, Differ. Equations, 2007, vol. 43, no. 4, pp. 460–468.
Mehlitz, P. and Wachsmuth, G., The limiting normal cone to pointwise defined sets in Lebesgue spaces, Set-Valued Var. Anal., 2018, vol. 26, no. 3, pp. 449–467.
Filippov, A.F., Differentsial’nye uravneniya s razryvnoi pravoi chast’yu (Differential Equations with Discontinuous Right-Hand Side), Moscow: Nauka, 1985.
Yosida, K., Functional Analysis, Berlin–Heidelberg: Springer-Verlag, 1965. Translated under the title: Funktsional’nyi analiz, Moscow: Mir, 1967.
Kolmogorov, A.N. and Fomin, S.V., Elementy teorii funktsii i funktsional’nogo analiza (Elements of the Function Theory and Functional Analysis), Moscow: Nauka, 1968.
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Translated by V. Potapchouck
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Petrova, L.P., Pryadko, I.N. On Systems of Differential Equations with Constraints in the Form of Not Necessarily Convex Sets. Diff Equat 58, 1309–1317 (2022). https://doi.org/10.1134/S00122661220100020
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DOI: https://doi.org/10.1134/S00122661220100020