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On a nonlocal problem for fractional integrodifferential inclusions in Banach spaces

Zuomao Yan (2011)

Annales Polonici Mathematici

This paper investigates a class of fractional functional integrodifferential inclusions with nonlocal conditions in Banach spaces. The existence of mild solutions of these inclusions is determined under mixed continuity and Carathéodory conditions by using strongly continuous operator semigroups and Bohnenblust-Karlin's fixed point theorem.

On fourth-order boundary-value problems

Myelkebir Aitalioubrahim (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We show the existence of solutions to a boundary-value problem for fourth-order differential inclusions in a Banach space, under Lipschitz’s contractive conditions, Carathéodory conditions and lower semicontinuity conditions.

On granular derivatives and the solution of a granular initial value problem

Ildar Batyrshin (2002)

International Journal of Applied Mathematics and Computer Science

Perceptions about function changes are represented by rules like “If X is SMALL then Y is QUICKLY INCREASING.” The consequent part of a rule describes a granule of directions of the function change when X is increasing on the fuzzy interval given in the antecedent part of the rule. Each rule defines a granular differential and a rule base defines a granular derivative. A reconstruction of a fuzzy function given by the granular derivative and the initial value given by the rule is similar to Euler’s...

On periodic oscillations for a class of feedback control systems in Hilbert spaces

Nguyen Van Loi (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, by using the topological degree theory for multivalued maps and the method of guiding functions in Hilbert spaces we deal with the existence of periodic oscillations for a class of feedback control systems in Hilbert spaces.

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

Mikhail Kamenskii, Valeri Obukhovskii, Jen-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 semilinear multi-valued flow under constraints and the periodic problem

Ralf Bader (2000)

Commentationes Mathematicae Universitatis Carolinae

* * In the paper we will be concerned with the topological structure of the set of solutions of the initial value problem of a semilinear multi-valued system on a closed and convex set. Assuming that the linear part of the system generates a C 0 -semigroup we show the R δ -structure of this set under certain natural boundary conditions. Using this result we obtain several criteria for the existence of periodic solutions for the semilinear system. As an application the problem of controlled heat transfer...

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

Ralf Bader, Boris D. Gel'man, Mikhail Kamenskii, Valeri 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...

Optimal control of impulsive stochastic evolution inclusions

N.U. Ahmed (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions driven by vector measures. We use stochastic vector measures as controls adapted to an increasing family of complete sigma algebras and prove the existence of optimal controls.

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