In this paper, we study the existence of solutions for evolution problems of the form − du dr (t) ∈ A(t)u(t)+F (t, u(t))+f (t, u(t)), where, for each t, A(t) : D(A(t)) → 2 H is a maximal monotone operator in a Hilbert space H with continuous, Lipschitz or absolutely continuous variation in time. The perturbation f is separately integrable on [0, T ] and separately Lipschitz on H, while F is scalarly measurable and separately scalarly upper semicontinuous on H, with convex and weakly compact values. Several new applications are provided.

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