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A first-order evolution problem with maximal monotone operators
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1  LMPA Laboratory, Department of Mathematics, Mohammed Seddik Benyahia University, Jijel, Algeria
Academic Editor: Alberto Cabada (registering DOI)

In Hilbert spaces, we are interested in proving the existence of bounded variation continuous solutions to a first-order evolution problem involving time and state dependent maximal monotone operators with perturbations.
This new result is established, under a compactness assumption on the domain of the operators. As an example, we provide the corresponding existence result for the perturbed sweeping process.

Keywords: evolution problem, maximal monotone operator, bounded variation continuous, sweeping process.