Displaying similar documents to “On initial value problems for a class of first order impulsive differential inclusions”

On Semicontinuity in Impulsive Dynamical Systems

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...

On time reparametrizations and isomorphisms of impulsive dynamical systems

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).

A new continuous dependence result for impulsive retarded functional differential equations

Márcia Federson, Jaqueline Godoy Mesquita (2016)

Czechoslovak Mathematical Journal

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We consider a large class of impulsive retarded functional differential equations (IRFDEs) and prove a result concerning uniqueness of solutions of impulsive FDEs. Also, we present a new result on continuous dependence of solutions on parameters for this class of equations. More precisely, we consider a sequence of initial value problems for impulsive RFDEs in the above setting, with convergent right-hand sides, convergent impulse operators and uniformly convergent initial data. We assume...

On nonresonance impulsive functional nonconvex valued differential inclusions

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.

On the existence of solutions for nonlinear impulsive periodic viable problems

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].

An existence result for impulsive functional differential inclusions in Banach spaces

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.