MULTI-VALUED PERTURBATION TO EVOLUTION PROBLEMS INVOLVING TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

In this paper, we study the existence of solutions for evolution problems of the form -du/dr (t) is an element of 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.