Abstract
A differential inclusion with a time-dependent maximal monotone operator and a perturbation is studied in a separable Hilbert space. The perturbation is the sum of a time-dependent single-valued operator and a multivalued mapping with closed nonconvex values. A particular feature of the single-valued operator is that its sum with the identity operator multiplied by a positive square-integrable function is a monotone operator. The multivalued mapping is Lipschitz continuous with respect to the phase variable. We prove the existence of a solution and the density in the corresponding topology of the solution set of the initial inclusion in the solution set of the inclusion with a convexified multivalued mapping. For these purposes, new distances between maximal monotone operators are introduced.
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Translated by I. Ruzanova
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Tolstonogov, A.A. Existence and Relaxation of Solutions for a Differential Inclusion with Maximal Monotone Operators and Perturbations. Dokl. Math. 108, 477–480 (2023). https://doi.org/10.1134/S1064562423701399
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DOI: https://doi.org/10.1134/S1064562423701399