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On initial value problems for a class of first order impulsive differential inclusions

100%

Benchohra M. , Boucherif A. , Nieto J.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2001

tom 21

nr 2

159-171

We investigate the existence of solutions to first order initial value problems for differential inclusions subject to impulsive effects. We shall rely on a fixed point theorem for condensing maps to prove our results.

On an hyperbolic functional differential inclusion in Banach spaces

75%

Benchohra M. , Ntouyas S. K.

Fasciculi Mathematici

2002

tom Nr 33

27-35

In this paper we investigate the existence of solutions to an hyperbolic functional differential inclusion in Banach spaces. We shall rely on a fixed point theorem for condensing maps due to of Martelli.

An existence result for hyperbolic functional differential inclusions

75%

Benchohra M. , Ntouyas S. K.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2002

tom [Z] 42(1)

1-16

In this paper we investigate the existence of solutions on an unbounded domain to an hyperbolic differential inclusion in Banach spaces. We shall rely on a fixed point theorem due to Ma, which is an extension to multivalued on locally convex topological spaces, of Schaefer's theorem.

An existence theorem for an hyperbolic differential inclusion in Banach spaces

75%

Benchohra M. , Ntouyas S.

nr 1

5-16

In this paper, we investigate the existence of solutions on unbounded domain to a hyperbolic differential inclusion in Banach spaces. We shall rely on a fixed point theorem due to Ma which is an extension to multivalued between locally convex topological spaces of Schaefer's theorem.

An abstract Cauchy problem for higher order functional differential inclusions with infinite delay

63%

Ke T. , Obukhovskii V. , Wong N.-C. , Yao J.-C.

tom 31

nr 2

199-229

The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our results. An application to some classes of partial differential equations is given.

On the topological dimension of the solutions sets for some classes of operator and differential inclusions

63%

Bader R. , Gel'man B. , Kamenskii M. , Obukhovskii V.

nr 1

17-32

In the present paper, we give the lower estimation for the topological dimension of the fixed points set of a condensing continuous multimap in a Banach space. The abstract result is applied to the fixed point set of the multioperator of the form $𝓕 = S 𝓟_F$ where $𝓟_F$ is the superposition multioperator generated by the Carathéodory type multifunction F and S is the shift of a linear injective operator. We present sufficient conditions under which this set has the infinite topological dimension. In the last section of the paper, we consider the applications of the solutions sets for Cauchy and periodic problems for semilinear differential inclusions in a Banach space.

On some topological methods in theory of neutral type operator differential inclusions with applications to control systems

63%

Kamenskii M. , Obukhovskii V. , Yao J.-C.

tom 33

nr 2

193-204

We consider a neutral type operator differential inclusion and apply the topological degree theory for condensing multivalued maps to justify the question of existence of its periodic solution. By using the averaging method, we apply the abstract result to an inclusion with a small parameter. As example, we consider a delay control system with the distributed control.