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Along this paper, we study an evolution inclusion governed by the so-called sweeping process. The right side of the inclusion contains a set-valued perturbation, supposed to be the external forces exercised on the system. We prove existence and relaxation results under weak assumptions on the perturbation by taking a truncated Lipschitz condition. These perturbations have non-convex and unbounded values without any compactness condition; we just assume a linear growth assumption on the element of minimal norm. The approach is based on the construction of approximate solutions. The relaxation is obtained by proving the density of the solution set of the original problem in a closure of the solution set of the relaxed one.

In this paper, we consider a perturbed sweeping process for a class of subsmooth moving sets. The perturbation is general and takes the form of a sum of a single-valued mapping and a set-valued mapping. In the first result, we study some topological proprieties of the attainable set, the set-valued mapping considered here is upper semi-continuous with convex values. In the second result, we treat the autonomous problem under assumptions that do not require the convexity of the values and that weaken the assumption on the upper semi-continuity. Then, we deduce a solution of the time optimality problem.

In this paper, we consider a first-order iterative differential inclusion. We study the existence of solutions and some topological proprieties of the attainable set, where the right hand side is an upper semi-continuous multifunction with convex values. Then, we treat the autonomous problem under assumptions that do not require the convexity of the values and that weaken the assumption on the upper semi-continuity. [ABSTRACT FROM AUTHOR]

The paper deals with quadratic optimal control problems, we study the equivalence between well-posed problems and affinity on the control for a second-order differential inclusions with two-points conditions, governed by a maximal monotone operator in a finite dimensional space. [ABSTRACT FROM AUTHOR]

Through this article, we aim to identify sufficient conditions to study the existence of solutions to a perturbed first-order iterative differential inclusion with maximal monotone operator. We provided examples to demonstrate our results. [ABSTRACT FROM AUTHOR]

We establish, in the setting of an infinite dimensional Hilbert space, results concerning the existence of solutions of second order "nonconvex sweeping process" for a class of uniformly prox-regular sets depending on time and state. The perturbation considered here is general and takes the form of a sum of a single-valued Carathéodory mapping and a set-valued unbounded mapping. We deal also with a delayed perturbation, that is the external forces applied on the system in presence of a finite delay. We extend a discretization approach known for the time-dependent case to the time and state-dependent sweeping process. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence of solution for an evolution inclusion of the form --...(t) ∈ ∂ φ(t, x(t)) + G(t,r(t)x) where ∂ φ (., .) is a subdifferential of a proper convex lower semicontinous function ∂ and G (., .) is a set-valued unbounded perturbation with nonempty convex closed values with delay. [ABSTRACT FROM AUTHOR]

In this work, we introduce a new concept of semi-continuous set-valued mappings, called almost mixed semi-continuity, by taking maps that are upper semi-continuous with almost convex values in some points and lower semi-continuous in remaining points. We generalize earlier results obtained for both mixed semi-continuous maps and almost convex sets. We discuss the existence of solution for evolution problems driven by the so-called sweeping process subject to external forces, known as perturbation to the system, by this type of set-valued mappings. Finally, we give some topological properties of the attainable and solution sets in order to solve an optimal time problem. [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]