Abstract
We consider some questions on G-convergence of a sequence of Nemytskii maximal monotone operators defined on the space of square integrable functions acting from a real interval to a separable Hilbert space. Every Nemytskii operator is generated by a time dependent family of maximal monotone operators. The values of these maximal monotone operators are normal cones of closed convex sets. These sets are values of a multivalued mapping from a real interval to a separable Hilbert space. The convergence of Nemytskii maximal monotone operators is used to study the dependence of solutions to sweeping processes on a parameter.
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Tolstonogov, A.A. Convergence of maximal monotone operators in a Hilbert space. Nonlinear Differ. Equ. Appl. 29, 69 (2022). https://doi.org/10.1007/s00030-022-00801-3
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DOI: https://doi.org/10.1007/s00030-022-00801-3