On a second-order functional evolution problem with time and state dependent maximal monotone operators. (English) Zbl 1493.34171
Summary: 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.
MSC:
| 34K09 | Functional-differential inclusions |
| 49J52 | Nonsmooth analysis |
| 49J53 | Set-valued and variational analysis |
Keywords:
differential inclusion; second-order; maximal monotone operator; delay; bounded variation continuous; pseudo-distanceReferences:
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