where H is a Hilbert space, and where F : T ×H → H is a set-valued mapping with nonempty compact values (some results hold also with no compactness assumption). It is well known that the differential inclusion description under consideration is important for its own sake and covers many other conventional and nonconventional models involving dynamical systems in finite and infinite dimensions. ...

Abstract Our main objectives in this paper are to investigate the existence of solutions for an integro-differential inclusion second order with hybrid nonlocal boundary value conditions. The sufficient condition uniqueness solution will be given and continuous dependence on set selections other functions proved. As application, problem Chandrasekhar second-order functional integrodifferential ...

The existence of solutions for a nonlinear fractional order differential inclusion is investigated. Several results are obtained by using suitable fixed point theorems when the right hand side has convex or non convex values.

The Non Smooth Dynamical Systems (NSDS) are a very special kind of dynamical systems characterized by their nonsmoothness in the evolution with respect to time and by a set of non smooth generalized equations. The so-called Moreau’s Sweeping Process[9, 10] is a special kind of differential inclusion with a maximal monotone operator[5] which appears to be a very nice formulation for the unilater...

where [f̂(x,K)]α e [X0] α are the α−levels of the fuzzy subsets f̂(x,K) and X̃0, respectively. As in [1] we saw that for each t > 0, the attainable set obtained under the Hüllermeier’s interpretation for (2), or rather, through a family of differential inclusions of the type gives in (3) coincides with the solution obtained applying the principle extension of Zadeh in deterministic solution We wil...

This paper studies the task-space coordinated tracking of a time-varying leader for multiple heterogeneous manipulators (MHMs), containing redundant manipulators and nonredundant ones. Different from the traditional coordinated control, distributed controller-estimator algorithms (DCEA), which consist of local algorithms and networked algorithms, are developed for MHMs with parametric uncertain...

The paper is devoted to determine necessary and sufficient conditions for existence of solutions to the problem inf { ess sup x∈Ω f(∇u(x)) : u ∈ u0 +W 1,∞ 0 (Ω) } , when the supremand f is not necessarily level convex. These conditions are obtained through a comparison with the related level convex problem and are written in terms of a differential inclusion involving the boundary datum. Severa...

We study the Cauchy problem for differential equations, considering its parameters and/or initial conditions given by fuzzy sets. These fuzzy differential equations are approached in two different ways: (a) by using a family of differential inclusions; and (b) the Zadeh extension principle for the solution of the model. We conclude that the solutions of the Cauchy problem obtained by both are t...

Using Bressan-Colombo results, concerning the existence of continuous selections of lower semicontinuous multifunctions with decomposable values, we prove a continuous version of Filippov’s theorem for a SturmLiuoville differential inclusion. This result allows to obtain a continuous selection of the solution set of the problem considered.

We prove a theorem on the existence of solutions of a second order differential inclusion governed by a class of nonconvex sweeping process with a mixed semicontinuous perturbation.