Evolution problems involving state-dependent maximal monotone operators

The main objective of the present paper is to prove the existence of absolutely continuous solutions for an evolution problem in a Hilbert space H, of the form (Formula presented.) where, for each (Formula presented.), the maximal monotone operator (Formula presented.) is of absolutely continuous variation in time and Lipschitz continuous in state, in the sense of the pseudo-distance introduced by A. A. Vladimirov. The perturbed problem is also considered.