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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces

100%
Benchohra M., Górniewicz L., Ntouyas S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2001
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tom 21
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nr 2
261-282
EN
In this paper, we shall establish sufficient conditions for the controllability on semi-infinite intervals for first and second order functional differential inclusions in Banach spaces. We shall rely on a fixed point theorem due to Ma, which is an extension on locally convex topological spaces, of Schaefer's theorem. Moreover, by using the fixed point index arguments the implicit case is treated.
2
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Semilinear evolution equations of the parabolic type

100%
Bochenek J.
Annales Polonici Mathematici
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1999
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tom 72
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nr 3
197-206
EN
This paper is devoted to the investigation of the abstract semilinear initial value problem du/dt + A(t)u = f(t,u), u(0) = u₀, in the "parabolic" case.
3
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Representation of the set of mild solutions to the relaxed semilinear differential inclusion

88%
Benedetti I., Panasenko E.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2006
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tom 26
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nr 1
143-158
EN
We study the relation between the solutions set to a perturbed semilinear differential inclusion with nonconvex and non-Lipschitz right-hand side in a Banach space and the solutions set to the relaxed problem corresponding to the original one. We find the conditions under which the set of solutions for the relaxed problem coincides with the intersection of closures (in the space of continuous functions) of sets of δ-solutions to the original problem.
4
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Controllability for impulsive semilinear functional differential inclusions with a non-compact evolution operator

75%
Benedetti I., Obukhovskii V., Zecca P.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2011
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tom 31
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nr 1
39-69
EN
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 on the jump functions. As example, we consider the controllability of an impulsive system governed by a wave equation with delayed feedback.
5
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An existence result for impulsive functional differential inclusions in Banach spaces

75%
Benedetti I.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2004
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tom 24
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nr 1
13-30
EN
We use the topological degree theory for condensing multimaps to present an existence result for impulsive semilinear functional differential inclusions in Banach spaces. Moreover, under some additional assumptions we prove the compactness of the solution set.
6
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Existence results for impulsive semilinear fractional differential inclusions with delay in Banach spaces

75%
Hammouche H., Guerbati K., Benchohra M., Abada N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2013
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tom 33
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nr 2
149-170
EN
In this paper, we introduce a new concept of mild solution of some class of semilinear fractional differential inclusions of order 0 < α < 1. Also we establish an existence result when the multivalued function has convex values. The result is obtained upon the nonlinear alternative of Leray-Schauder type.
7
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Controllability of impulsive semilinear functional differential inclusions with finite delay in Fréchet spaces

75%
Abada N., Benchohra M., Hammouche H., Ouahab A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2007
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tom 27
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nr 2
329-347
EN
In this paper, we use the extrapolation method combined with a recent nonlinear alternative of Leray-Schauder type for multivalued admissible contractions in Fréchet spaces to study the existence of a mild solution for a class of first order semilinear impulsive functional differential inclusions with finite delay, and with operator of nondense domain in original space.
8
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Fractional integro-differential inclusions with state-dependent delay

75%
Aissani K., Benchohra M., Ezzinbi K.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2014
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tom 34
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nr 2
153-167
EN
In this paper, we establish sufficient conditions for the existence of mild solutions for fractional integro-differential inclusions with state-dependent delay. The techniques rely on fractional calculus, multivalued mapping on a bounded set and Bohnenblust-Karlin's fixed point theorem. Finally, we present an example to illustrate the theory.
9
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Global Existence and Stability for Neutral Functional Evolution Equations with State-Dependent Delay

75%
Baliki A., Benchohra M.
Nonautonomous Dynamical Systems
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2014
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tom 1
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nr 1
EN
In this paper we prove the global existence and attractivity of mild solutions for neutral semilinear evolution equations with state-dependent delay in a Banach space.
10

Existence of mild solutions on infinite intervals to first order initial value problems for a class of differential inclusions in banach spaces

75%
Benchohra M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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1999
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tom 19
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nr 1-2
111-121
EN
In this paper we investigate the existence of mild solutions on an unbounded real interval to first order initial value problems for a class of differential inclusions in Banach spaces. We shall make use of a theorem of Ma, which is an extension to multivalued maps on locally convex topological spaces of Schaefer's theorem.
11
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Pseudo almost periodic and automorphic mild solutions to nonautonomous neutral partial evolution equations

63%
Akdad A.-N., Ezzinbi K., Souden L.
Nonautonomous Dynamical Systems
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2015
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tom 2
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nr 1
EN
In this work, we present a new concept of Stepanov weighted pseudo almost periodic and automorphic functions which is more generale than the classical one, and we obtain a new existence result of μ-pseudo almost periodic and μ-pseudo almost automorphic mild solutions for some nonautonomous evolution equations with Stepanov μ-pseudo almost periodic terms. An example is shown to illustrate our results.
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