Some features of uncontinuable solutions of impulsive dynamical systems.
H. D. Dimov, S. I. Nenov (1996)
Extracta Mathematicae
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H. D. Dimov, S. I. Nenov (1996)
Extracta Mathematicae
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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...
Shi, Ruiqing, Chen, Lansun (2007)
Discrete Dynamics in Nature and Society
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Daniel Franco, Juan J. Nieto, Yuri V. Rogovchenko (1998)
Extracta Mathematicae
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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).
Byszewski, Ludwik (1993)
Journal of Applied Mathematics and Stochastic Analysis
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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.
Jiao, Jianjun, Chen, Lansun (2010)
Advances in Difference Equations [electronic only]
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Wang, Weibing, Shen, Jianhua, Nieto, Juan J. (2007)
Discrete Dynamics in Nature and Society
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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...
D. D. Bainov, S. I. Kostadinov, A. D. Myshkis (1990)
Publicacions Matemàtiques
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By means of Schauder's fixed point theorem sufficient conditions for asymptotic equivalence of impulsive equations in a Banach space are found.
Jiao, Jianjun (2010)
Discrete Dynamics in Nature and Society
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Changming Ding (2014)
Annales Polonici Mathematici
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We investigate a Lotka-Volterra predator-prey model with state dependent impulsive effects, in which the control strategies by releasing natural enemies and spraying pesticide at different thresholds are considered. We present some sufficient conditions to guarantee the existence and asymptotical stability of semi-trivial periodic solutions and positive periodic solutions.
Liu, Kaiyuan, Chen, Lansun (2008)
Discrete Dynamics in Nature and Society
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