Mouffak Benchohra, Abdelkader Boucherif, Juan J. Nieto (2001)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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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.
Krzysztof Ciesielski (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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In the important paper on impulsive systems [K1] several notions are introduced and several properties of these systems are shown. In particular, the function ϕ which describes "the time of reaching impulse points" is considered; this function has many important applications. In [K1] the continuity of this function is investigated. However, contrary to the theorem stated there, the function ϕ need not be continuous under the assumptions given in the theorem. Suitable examples are shown...
H. D. Dimov, S. I. Nenov (1996)
Extracta Mathematicae
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Irene Benedetti (2004)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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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.
Mouffak Benchohra, Johnny Henderson, Sotiris K. Ntouyas (2002)
Commentationes Mathematicae Universitatis Carolinae
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In this paper a fixed point theorem for contraction multivalued maps due to Covitz and Nadler is used to investigate the existence of solutions for first and second order nonresonance impulsive functional differential inclusions in Banach spaces.
Benchohra, M., Graef, J.R., Henderson, J., Ntouyas, S.K. (2002)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Nadjet Abada, Ravi P. Agarwal, Mouffak Benchohra, Hadda Hammouche (2011)
Applications of Mathematics
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In this paper we establish sufficient conditions for the existence of mild solutions and extremal mild solutions for some densely defined impulsive semilinear neutral functional differential inclusions in separable Banach spaces. We rely on a fixed point theorem for the sum of completely continuous and contraction operators.
Krzysztof Ciesielski (2004)
Annales Polonici Mathematici
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We prove that for a given impulsive dynamical system there exists an isomorphism of the basic dynamical system such that in the new system equipped with the same impulse function each impulsive trajectory is global, i.e. the resulting dynamics is defined for all positive times. We also prove that for a given impulsive system it is possible to change the topology in the phase space so that we may consider the system as a semidynamical system (without impulses).
Tiziana Cardinali, Raffaella Servadei (2004)
Open Mathematics
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In this paper we prove the existence of periodic solutions for nonlinear impulsive viable problems monitored by differential inclusions of the type x′(t)∈F(t,x(t))+G(t,x(t)). Our existence theorems extend, in a broad sense, some propositions proved in [10] and improve a result due to Hristova-Bainov in [13].