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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)) → 2H, is a maximal monotone operator in a Hilbert space H with continuous, Lipschitz or absolutely continuous variation in time. The perturbation ƒ 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. [ABSTRACT FROM AUTHOR]

Using an explicit catching-up algorithm, we prove the existence of absolutely continuous as well as bounded variation continuous solutions to a second-order perturbed Moreau's sweeping process with the normal cone of a subsmooth moving set, which depends both on the time and on the state. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of evolution problems involving fractional flow and time and state dependent maximal monotone operator which is absolutely continuous in variation with respect to the Vladimirov's pseudo distance. In a first part, we solve a second order problem and give an application to sweeping process. In a second part, we study a class of fractional order problem driven by a time and state dependent maximal monotone operator with a Lipschitz perturbation in a separable Hilbert space. In the last part, we establish a Filippov theorem and a relaxation variant for fractional differential inclusion in a separable Banach space. In every part, some variants and applications are presented. [ABSTRACT FROM AUTHOR]