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doi: 10.3934/eect.2021034
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## On a second-order functional evolution problem with time and state dependent maximal monotone operators

 LMPA Laboratory, Department of Mathematics, Mohammed Seddik Ben Yahia University, Jijel-Algeria

Received  December 2020 Revised  May 2021 Early access July 2021

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.

Citation: Soumia Saïdi. On a second-order functional evolution problem with time and state dependent maximal monotone operators. Evolution Equations and Control Theory, doi: 10.3934/eect.2021034
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