Perturbed Evolution Problems with Continuous Bounded Variation in Time and Applications

This paper is devoted to the study of evolution problems of the form − du dr ( t ) ∈ A ( t ) u ( t ) + f ( t , u ( t ) ) in a new setting, where, for each t , A ( t ) : D ( A ( t )) → 2 H is a maximal monotone operator in a Hilbert space H and the mapping t ↦ A ( t ) has continuous bounded or Lipschitz variation on [0, T ], in the sense of Vladimirov’s pseudo-distance. The measure dr gives an upper bound of that variation. The perturbation f is separately integrable on [0, T ] and separately Lipschitz on H . Several versions and new applications are presented.