This paper studies the system stability problems of a class of nonconvex differential inclusions. At first, a basic stability result is obtained by virtue of locally Lipschitz continuous Lyapunov functions. Moreover, a generalized invariance principle and related attraction conditions are proposed and proved to overcome the technical difficulties due to the absence of convexity. In the technica...

We consider a semilinear differential inclusion and we obtain sufficient conditions for h-local controllability along a reference trajectory.

In this paper we examine nonlinear integrodifferential inclusions defined in a separable Banach space. Using a compactness type hypothesis involving the ball measure of noncompactness, we establish two existence results. One involving convex-valued orientor fields and the other nonconvex valued ones.

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.