Multiple positive solutions for nonlinear first-order impulsive dynamic equations on time scales with parameter.
Wang, Da-Bin, Guan, Wen (2009)
Advances in Difference Equations [electronic only]
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Wang, Da-Bin, Guan, Wen (2009)
Advances in Difference Equations [electronic only]
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Mouffak Benchohra, Samira Hamani, Johnny Henderson (2007)
Archivum Mathematicum
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In this paper we discuss the existence of oscillatory and nonoscillatory solutions for first order impulsive dynamic inclusions on time scales. We shall rely of the nonlinear alternative of Leray-Schauder type combined with lower and upper solutions method.
H. D. Dimov, S. I. Nenov (1996)
Extracta Mathematicae
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Benchohra, Mouffak, Hamani, Samira, Henderson, Johnny (2006)
Advances in Difference Equations [electronic only]
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Atici, F.M., Biles, D.C. (2005)
Advances in Difference Equations [electronic only]
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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...
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.
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...
Bainov, D.D., Stamova, I.M. (1999)
Journal of Applied Mathematics and Stochastic Analysis
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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).