Impulsive Differential Inclusions Research Articles

Controllability of impulsive neutral functional differential inclusions with infinite delay in Banach spaces

In this work, we establish a sufficient condition for the controllability of the first-order impulsive neutral functional differential inclusions with infinite delay in Banach spaces. The results are obtained by using the Dhage’s fixed point theorem.

Impulsive Boundary Value Problems for First-order Ordinary Differential Inclusions

In this paper, we investigate the existence of solutions for impulsive first order ordinary differential inclusions which admitting nonconvex valued right hand side. We present two classes of results. In the first one, we rely on a fixed point theorem for contraction multivalued maps due to Covitz and Nadler, and for the second one, we use Schaefer's fixed point theorem combined with lower semi-continuous multivalued operators with decomposable values under weaker conditions.

Averaging of impulsive differential inclusions with Hukuhara derivative

We substantiate the method of complete or partial averaging for differential inclusions that contain the Hukuhara derivative and are subject to pulse influence at fixed times.

Impulsive semilinear differential inclusions: Topological structure of the solution set and solutions on non-compact domains

This paper deals with an impulsive Cauchy problem governed by the semilinear evolution differential inclusion x ′ ( t ) ∈ A ( t ) x ( t ) + F ( t , x ( t ) ) , where { A ( t ) } t ∈ [ 0 , b ] is a family of linear operators (not necessarily bounded) in a Banach space E generating an evolution operator and F is a Carathéodory type multifunction. First a theorem on the compactness of the set of all mild solutions for the problem is given. Then this result is applied to obtain the existence of mild solutions for the impulsive Cauchy problem defined on non-compact domains.

Existence for neutral impulsive differential inclusions with nonlocal conditions

In this paper, by using a fixed point theorem for condensing multi-valued maps, we have investigated the existence of mild solutions for a class of semilinear impulsive neutral functional differential inclusions with nonlocal conditions. As an application, an example has been presented to illustrate the results obtained.

Controllability of impulsive semilinear functional differential inclusions with finite delay in Fréchet spaces

Controllability of impulsive semilinear functional differential inclusions with finite delay in Fréchet spaces

Extrapolation spaces and controllability of impulsive semilinear functional differential inclusions with infinite delay in Fréchet spaces

In this article, we investigate some classes of semilinear impulsive functional differential inclusions with infinite delay. It is assumed that the linear part is possibly neither densely defined nor it satisfies the Hille–Yosida condition on a Banach space, namely the extrapolated space. Our approach is based on the theory of extrapolation spaces combined with a recent Frigon nonlinear alternative for multivalued admissible contractions in Fréchet spaces.

Approximation of a bundle of solutions of linear differential inclusions

We construct an approximation of a bundle of solutions of a linear impulsive differential inclusion using a system of linear impulsive differential equations with Hukuhara derivative.

Existence theory for perturbed impulsive hyperbolic differential inclusions with variable times

In this paper, the existence of solutions for a perturbed impulsive hyperbolic differential inclusion with variable times is proved under the mixed generalized Lipschitz and Carathéodory's conditions.

Solution bundle for a class of impulsive differential inclusions on Banach spaces

In this paper a class of impulsive differential inclusions is investigated. The existence of solution bundle is proved. And we also construct a nonlinear semigroup of operators on cb ( E ) (closed-bounded subset of E) to describe the set of attainable states.

A comment on the papers: Controllability results for functional semilinear differential inclusions in Fréchet spaces [Nonlinear Anal. 61 (3) (2005) 405–423] and Controllability of impulsive neutral functional differential inclusions with infinite delay [Nonlinear Anal. 60 (8) (2005) 1533–1552

In this note we make some observations relating two papers recently published in Nonlinear Analysis Theory, Methods & Applications.

Existence results for second-order impulsive functional differential inclusions

The existence of solutions on a compact interval to second-order impulsive functional differential inclusions is investigated. Several new results are obtained by using Sadovskii's fixed point theorem.

Periodic solutions to impulsive differential inclusions with constraints

The existence of a periodic solution to an impulsive differential inclusion being invariant with respect to a non-convex set of state constraints is established by the use a Lefschetz type fixed-point theorem for set-valued maps.

Measure solutions for impulsive evolution equations with measurable vector fields

In this paper we present some results on the question of existence of generalized or measure valued solutions for semilinear impulsive evolution equations on Banach spaces with the nonlinear parts being merely measurable and bounded on bounded sets. This is a far reaching generalization of the previous results of the author and others. It may be interesting to consider extension of the results of this paper to cover impulsive differential inclusions and their potential applications to control theory and uncertain dynamics.

Existence results for first and second order semilinear impulsive differential inclusions

In this paper we prove existence results for first and second order semilinear impulsive differential inclusions in Banach spaces.

Existence results for impulsive neutral functional differential inclusions

In this paper we prove existence results for first and second order impulsive neutral functional differential inclusions under the mixed Lipschitz and Caratheodory conditions.

Set-valued solutions to impulsive differential inclusions

This paper deals with the state estimation problem for impulsive control systems described by differential inclusions with measures. The problem is studied under uncertainty conditions with set-membership description of uncertain variables which are taken to be unknown but bounded with given bounds. Such problems arise from mathematical models of dynamical and physical systems for which we have an incomplete description of their generalized coordinates (e.g. the model may contain unpredictable errors without their statistical description). In this setting instead of an isolated trajectory of the dynamical control system we have a tube of such trajectories and the phase state vector should be replaced by the set of its possible values. The techniques of constructing the trajectory tubes and their cross-sections that may be considered as set-valued state estimates to differential inclusions with impulses are studied.

Controllability of impulsive neutral functional differential inclusions with infinite delay

The paper is concerned with the controllability of the first-order impulsive neutral functional differential inclusions with infinite delay in a Banach space. Sufficient conditions for controllability are obtained by using a fixed point theorem for condensing maps due to Martelli. As an application, we also consider an impulsive neutral partial functional differential equation.

Existence of solutions to initial value problems for the second order mixed monotone type of impulsive differential inclusions

In this paper we consider the initial value problems for the second order mixed monotone type of impulsive differential inclusions. By introducing a special partial order, we present the existence of maximal and minimal fixed points for mixed monotone multivalued operators in Banach spaces. Applying the results, we establish the existence and uniqueness of above impulsive differential inclusions.

Controllability results for impulsive functional differential inclusions

Control problems appear in many branches of physics and technical sciences. In this paper weinvestigate the controllability of first order semilinear impulsive functional differential inclusions in the case where the right hand side is convex or nonconvex valued. All results are obtained by using fixed point results for multivalued mappings.