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Controllability for impulsive semilinear functional differential inclusions with a non-compact evolution operator

Irene BenedettiValeri ObukhovskiiPietro Zecca — 2011

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We study a controllability problem for a system governed by a semilinear functional differential inclusion in a Banach space in the presence of impulse effects and delay. Assuming a regularity of the multivalued non-linearity in terms of the Hausdorff measure of noncompactness we do not require the compactness of the evolution operator generated by the linear part of inclusion. We find existence results for mild solutions of this problem under various growth conditions on the nonlinear part and...

Multivalued linear operators and differential inclusions in Banach spaces

Anatolii BaskakovValeri ObukhovskiiPietro Zecca — 2003

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we study multivalued linear operators (MLO's) and their resolvents in non reflexive Banach spaces, introducing a new condition of a minimal growth at infinity, more general than the Hille-Yosida condition. Then we describe the generalized semigroups induced by MLO's. We present a criterion for an MLO to be a generator of a generalized semigroup in an arbitrary Banach space. Finally, we obtain some existence results for differential inclusions with MLO's and various types of multivalued...

On the topological structure of the solution set for a semilinear ffunctional-differential inclusion in a Banach space

Giuseppe ContiValeri ObukhovskiĭPietro Zecca — 1996

Banach Center Publications

In this paper we show that the set of all mild solutions of the Cauchy problem for a functional-differential inclusion in a separable Banach space E of the form x’(t) ∈ A(t)x(t) + F(t,xt) is an R δ -set. Here A(t) is a family of linear operators and F is a Carathéodory type multifunction. We use the existence result proved by V. V. Obukhovskiĭ [22] and extend theorems on the structure of solutions sets obtained by N. S. Papageorgiou [23] and Ya. I. Umanskiĭ [32].

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

Mikhail KamenskiiValeri ObukhovskiiJen-Chih Yao — 2013

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

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

Ralf BaderBoris D. Gel'manMikhail KamenskiiValeri Obukhovskii — 2002

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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 = S F where 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...

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

Tran Dinh KeValeri ObukhovskiiNgai-Ching WongJen-Chih Yao — 2011

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

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