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In this paper we establish, in a separable Hilbert space, a result asserting the existence of absolutely continuous solutions for a system made up of a first-order differential inclusion governed by time and state-dependent maximal monotone operators; and an ordinary differential equation. From this result, we derive existence of absolutely continuous solutions to a second-order differential inclusion governed by time and state-dependent maximal monotone operators. [ABSTRACT FROM AUTHOR]

In this paper we prove, in a separable Hilbert space, the existence of solutions to a couple of differential inclusions, both of them governed by time and state-dependent maximal monotone operators, and with multi-valued perturbations. An application to an optimal control problem is also presented. [ABSTRACT FROM AUTHOR]

In this paper we establish the existence and uniqueness result of right continuous bounded variation solution for a perturbed differential inclusion governed by time-dependent maximal monotone operators. [ABSTRACT FROM AUTHOR]

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 − (d u / d t) (t) ∈ A (t , u (t)) u (t) where, for each (t , x) ∈ [ 0 , T ] × H , the maximal monotone operator A (t , x) : H → 2 H 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. [ABSTRACT FROM AUTHOR]

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]

This paper is devoted to the study of evolution problems of the form −dudr(t)∈A(t)u(t)+f(t,u(t)) in a new setting, where, for each t, A(t) : D(A(t)) → 2H 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. [ABSTRACT FROM AUTHOR]

In this work, we study the existence of solutions of a perturbed sweeping process and of a time optimal control problem under a condition on the perturbation that is strictly weaker than the usual assumption of convexity. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a perturbed differential inclusion governed by a sweeping process in a Hilbert space. The sweeping process is perturbed by a sum of a single-valued map satisfying a Lipschitz condition and a scalarly upper semicontinuous set-valued map. [ABSTRACT FROM AUTHOR]

We study the existence of solutions of a three-point boundary-value problem for a second-order differential inclusion, ü(t) ∈ F(t, u(t), u̇(t)), a.e. t ∈ [0, 1], u(0) = 0, u(θ) = u(1). Here F is a set-valued mapping from [0, 1] x E x E to E with nonempty closed values satisfying a standard Lipschitz condition, and E is a separable Banach space. [ABSTRACT FROM AUTHOR]

This paper provide some applications of Pettis integration to differential inclusions in Banach spaces with three point boundary conditions of the form ü(t) ε F(t, u(t),ù (t)) + H(t, u(t)), ù(t)), a.e. t ε [0, 1], where F is a convex valued multifunction upper semicontinuous on E x E and H is a lower semicontinuous multifunction. The existence of solutions is obtained under the non convexity condition for the multifunction H, and the assumption that F(t, x, y) ⊂Г1(t), H(t, x, y) ⊂Г2(t), where the multifunctions Г1, Г2 : [0, 1]⇒ E are uniformly Pettis integrable. [ABSTRACT FROM AUTHOR]