The existence of an absolutely continuous solution of a differential inclusion whose right-hand side contains a time- and state-dependent maximal monotone operator and a nonconvex perturbation is proved in a Hilbert space. The proofs are based on our comparison theorems for inclusions with maximal monotone operators and a fixed point theorem for multivalued mappings. This approach allows us to extend the class of inclusions with maximal monotone operators for which existence theorems are valid and, as a result, to obtain significant results of this kind.
Keywords: maximal monotone operator, $G$-convergence, comparison theorem
Received April 4, 2024
Revised May 15, 2024
Accepted May 20, 2024
Alexander Alexandrovich Tolstonogov, Corresponding member of RAS, Dr. Phys.-Math. Sci., Prof., Matrosov Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences, Irkutsk, 664033 Russia, e-mail: alexander.tolstonogov@gmail.com
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Cite this article as: A.A. Tolstonogov. Evolution inclusions with state-dependent maximal monotone operators. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2024, vol. 30, no. 3, pp. 241–254.
