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GENERALIZED ODE APPROACH TO IMPULSIVE RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS

机译:脉冲滞后泛函微分方程的广义ODE方法

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摘要

It is known that retarded functional differential equations (RFDEs) can be regarded as generalized ordinary differential equations (we write GOD13s). See [2, 6, 7]. In this paper, we prove the equivalence between RFDEs with pre-assigned moments of impulse effects and a certain class of GODEs introduced in [8] using some ideas of [2, 6, 7]. We state results on the existence, uniqueness and continuous dependence of solutions for this class of GODEs and we use them to obtain fine results concerning the corresponding impulsive RFDEs.
机译:众所周知,延迟泛函微分方程(RFDE)可以看作是广义的常微分方程(我们写GOD13s)。参见[2,6,7]。在本文中,我们使用[2,6,7]的一些思想证明了具有预分配的脉冲效应矩的RFDE与[8]中引入的特定类型的GODE之间的等效性。我们根据此类GODE的解的存在性,唯一性和连续依赖性来陈述结果,并使用它们来获得有关相应脉冲RFDE的优良结果。

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