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On a second-order functional evolution problem with time and state dependent maximal monotone operators

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  • The present paper proposes, in a real separable Hilbert space, to analyze the existence of solutions for a class of perturbed second-order state-dependent maximal monotone operators with a finite delay. The dependence of the operators is -in some sense- absolutely continuous (or bounded continuous) variation in time, and Lipschitz continuous in state. The approach to solve our problem is based on a discretization scheme. The uniqueness result is applied to optimal control.

    Mathematics Subject Classification: Primary: 34K09; Secondary: 49J52, 49J53.


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