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In this paper, we analyze and discuss the well-posedness of a new variant of the so-called sweeping process. In this variant, the prox-regular moving set C(t) is supposed to have an absolutely continuous variation and is perturbed by an integral forcing term. The integrand of the forcing term depends on two time-variables; that is, we study a general integro-differential sweeping process of Volterra type. The results are applied to nonregular electrical circuits containing timevarying capacitors and nonsmooth electronic devices like diodes. A circuit with transmission line, diode, and inductor is also analyzed. All these applications represent an additional novelty of our paper. [ABSTRACT FROM AUTHOR]

Projected differential equations are known as fundamental mathematical models in economics, for electric circuits, etc. The present paper studies the (higher order) derivability as well as a generalized type of derivability of solutions of such equations when the set involved for projections is prox-regular with smooth boundary. [ABSTRACT FROM AUTHOR]

In this article we discuss the differential inclusion known as state dependent sweeping process for a class of prox-regular non-convex sets. We associate with any state dependent sweeping process with such sets an unconstraint differential inclusion whose any solution is a solution of the state sweeping process too. We prove a theorem on the existence of a global solution of nonconvex state dependent sweeping process with unbounded perturbations. The perturbations are not required to be convex valued. [ABSTRACT FROM AUTHOR]

In this paper, we analyze and discuss the well-posedness of two new variants of the so-called sweeping process, introduced by Moreau in the early 70s (Moreau in Sém Anal Convexe Montpellier, ) with motivation in plasticity theory. The first new variant is concerned with the perturbation of the normal cone to the moving convex subset $$C(t)$$ , supposed to have a bounded variation, by a Lipschitz mapping. Under some assumptions on the data, we show that the perturbed differential measure inclusion has one and only one right continuous solution with bounded variation. The second variant, for which a large analysis is made, concerns a first order sweeping process with velocity in the moving set $$C(t)$$ . This class of problems subsumes as a particular case, the evolution variational inequalities [widely used in applied mathematics and unilateral mechanics (Duvaut and Lions in Inequalities in mechanics and physics. Springer, Berlin, ]. Assuming that the moving subset $$C(t)$$ has a continuous variation for every $$t\in [0,T]$$ with $$C(0)$$ bounded, we show that the problem has at least a Lipschitz continuous solution. The well-posedness of this class of sweeping process is obtained under the coercivity assumption of the involved operator. We also discuss some applications of the sweeping process to the study of vector hysteresis operators in the elastoplastic model (Krejčı in Eur J Appl Math 2:281-292, ), to the planning procedure in mathematical economy (Henry in J Math Anal Appl 41:179-186, and Cornet in J. Math. Anal. Appl. 96:130-147, ), and to nonregular electrical circuits containing nonsmooth electronic devices like diodes (Acary et al. Nonsmooth modeling and simulation for switched circuits. Lecture notes in electrical engineering. Springer, New York ). The theoretical results are supported by some numerical simulations to prove the efficiency of the algorithm used in the existence proof. Our methodology is based only on tools from convex analysis. Like other papers in this collection, we show in this presentation how elegant modern convex analysis was influenced by Moreau's seminal work. [ABSTRACT FROM AUTHOR]

In a separable Banach space we consider a three point boundary value problem for a second order differential inclusion of the form [image omitted] We investigate the existence of solutions, when the multifunction F is unbounded-valued and satisfies a pseudo-Lipschitz property. Then, a Lipschitz case is derived and the associated relaxed problem is studied. [ABSTRACT FROM AUTHOR]

In this paper we prove a theorem on the existence of a global solution of a differential inclusion governed by a class of nonconvex sweeping processes with unbounded pertubations. The perturbations are not required to be convex valued. [ABSTRACT FROM AUTHOR]

The article studies the three-point boundary value problems for second-order perturbed differential inclusions of the form [image omitted] a.e. on [0,1]. The existence of solutions is proved under nonconvexity condition for the multifunction H. [ABSTRACT FROM AUTHOR]

Differential inclusions involving the normal cone to a moving set are investigated. A special attention is paid to the sweeping process associated with sets for which no regularity assumption is required. [Copyright &y& Elsevier]