In this paper, the classic straightening out theorem from di erential geometry is used to derive necessary and su cient conditions for locally converting rectangular di erential inclusions to constant rectangular di erential inclusions. Both scalar and coupled di erential inclusions are considered. The results presented in this paper have use in the area of computer aided veri cation of hybrid ...

In this paper, we present an impulsive version of Filippov’s Theorem for fractional differential inclusions of the form: D ∗ y(t) ∈ F (t, y(t)), a.e. t ∈ J\{t1, . . . , tm}, α ∈ (1, 2], y(t+k )− y(t − k ) = Ik(y(t − k )), k = 1, . . . ,m, y(t+k )− y (t−k ) = Ik(y (t−k )), k = 1, . . . ,m, y(0) = a, y′(0) = c, where J = [0, b], D ∗ denotes the Caputo fractional derivative and F is a setvalued ma...

In this paper, we present an impulsive version of Filippov's Theorem for the first-order nonresonance impulsive differential inclusion y (t) − λy(t) ∈ F (t, y(t)), a.e. characterize the jump of the solutions at impulse points t k (k = 1,. .. , m.). Then the relaxed problem is considered and a Filippov-Wasewski result is obtained. We also consider periodic solutions of the first order impulsive ...

We study the existence of solutions for fractional differential inclusions of order q ∈ (1, 2] with four-point integral boundary conditions. We establish Filippov type existence results in the case of nonconvex set-valued maps. Full text

This paper presents a comparison between two abstract frameworks in which one can treat multi-valued semiflows and their asymptotic behaviour. We compare the theory developed by Ball (1997) to treat equations whose solutions may not be unique, and that due to Melnik and Valero (1998) tailored more for differential inclusions. Although they deal with different problems, the main ideas seem quite...

In this paper we are concerned with the study of a class of quasilinear elliptic differential inclusions involving the anisotropic − →p (·)-Laplace operator, on a bounded open subset of Rn which has a smooth boundary. The abstract framework required to study this kind of differential inclusions lies at the interface of three important branches in analysis: nonsmooth analysis, the variable expon...

Two existence results for monotone trajectories of diierential inclusions x 0 (t) 2 F ? t; x(t) in a separable Banach space are obtained; they extend in two directions previous ones due to Aubin-Cellina, Deimling and Haddad.

We present a new inverse mapping theorem for correspondences. It uses a notion of differentiability for multifunctions which seems to be new. We compare it with previous versions. We provide an application to differential inclusions.

Let X be a separable Banach space, σ > 0 and Cσ := C([−σ, 0],X) the Banach space of the continuous functions from [−σ, 0] into X, K a locally closed set in X and F : [a, b)×Cσ→ 2 X a closed valued and locally integrable bounded multifunction, withF (., φ) measurable and F (t, .) Lipschitz continuous in theHausdorff–Pompeiumetric. In this paper we establish some sufficient conditions in order th...

In this paper the stabilization problem of nonlinear uncertain systems described by diierential inclusions is considered. The nominal system is assumed to be aane in the control variable. For the stabilization of the nominal system, a variant of the receding horizon control method is proposed which is based on the solution of a certain Bolza problem. The results are illustrated by an example.