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.

This paper is devoted to the study of geometries of inhomogeneities with minimum strain or stress concentration. The solutions are achieved by the indirect method of first deriving lower bounds and then constructing the geometries to attain the lower bounds. In particular, we show that a new class of geometries, namely, E-inclusions and periodic E-inclusions, are the optimal geometries with min...

The existence of a continuum of many chaotic solutions is shown for certain differential inclusions which are small periodic multivalued perturbations of ordinary differential equations possessing homoclinic solutions to hyperbolic fixed points. Applications are given to dry friction problems. Singularly perturbed differential inclusions are investigated as well.

Necessary conditions of optimality are derived for multiobjective optimal control problems with pathwise state constraints, in which the dynamics constrain is modeled as a differential inclusion. The obtained result extends results of [2] and [29].