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Measure Neutral Functional Differential Equations as Generalized ODEs

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Abstract

In this paper, we introduce a class of measure neutral functional differential equations of type

$$\begin{aligned} \mathrm {D}[N(x_t,t)]=f(x_t,t)\mathrm {D}g(t) \end{aligned}$$

through the relation with a certain class of generalized ordinary differential equations introduced in Federson and Schwabik (Differ Integral Equ 19(11):1201–1234, 2006) (we write generalized ODEs), using similar ideas to those of Federson et al. (J Differ Equ 252(6):3816–3847, 2012). By means of the correspondence with generalized ODEs, we state results on the existence, uniqueness and continuous dependences of solutions for our equation of neutral type.

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Authors and Affiliations

  1. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Campus de São Carlos, Caixa Postal 668, 13560-970, São Carlos, SP, Brazil

    M. Federson & M. Frasson

  2. Instituto de Ciências Exatas, Universidade de Brasilia, Brasília, DF, Brazil

    J. G. Mesquita

  3. Faculdade de Ciências e Tecnologia, Universidade Estadual Paulista “Júlio de Mesquita Filho”, Presidente Prudente, SP, Brazil

    P. H. Tacuri

Authors
  1. M. Federson
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  2. M. Frasson
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  3. J. G. Mesquita
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  4. P. H. Tacuri
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Corresponding author

Correspondence to P. H. Tacuri.

Additional information

M. Federson: Supported by CNPq Grant 309344/2017-4 and FAPESP Grant 2017/13795-2. M. Frasson: Supported by CNPq Grant 152258/2010-8. J. G. Mesquita: Partially supported by CNPq Grant 407952/2016-0 and FEMAT-Fundação de Estudos em Ciências Matemáticas Proc. 039/2017. P. H. Tacuri: Supported by CNPq Grant 141947/2009-8.

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Federson, M., Frasson, M., Mesquita, J.G. et al. Measure Neutral Functional Differential Equations as Generalized ODEs. J Dyn Diff Equat 31, 207–236 (2019). https://doi.org/10.1007/s10884-018-9682-y

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  • DOI: https://doi.org/10.1007/s10884-018-9682-y

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