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Existence and Uniqueness of Solutions for Abstract Neutral Differential Equations with State-Dependent Delay

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Abstract

We study the existence and uniqueness of mild and strict solutions for abstract neutral differential equations with state-dependent delay. Some examples related to partial neutral differential equations are presented.

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Acknowledgements

The authors wish to thank the referees and the editor responsible for this paper, for their valuable comments and suggestions.

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Authors and Affiliations

  1. Departamento de Computação e Matemática, Faculdade de Filosofia Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Ribeirão Preto, SP, CEP 14040-901, Brazil

    Eduardo Hernández

  2. Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada

    Jianhong Wu

  3. Departamento de Matemática, Instituto de Biociências Letras e Ciências Exatas Universidade Estadual Paulista, São José do Rio Preto, SP, CEP 15054-000, Brazil

    Denis Fernandes

Authors
  1. Eduardo Hernández
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  2. Jianhong Wu
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  3. Denis Fernandes
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Correspondence to Eduardo Hernández.

Additional information

E. Hernández: This work was developed during my visit to York University, Canada and partially supported by Fapesp FAPESP, Grant 2014/25820-3, and by the Natural Sciences and Engineering Research Council of Canada. I would like to thank York University and Jianhong Wu for the collaboration and great hospitality. D. Fernandes: The work of this author was supported by CAPES.

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Hernández, E., Wu, J. & Fernandes, D. Existence and Uniqueness of Solutions for Abstract Neutral Differential Equations with State-Dependent Delay. Appl Math Optim 81, 89–111 (2020). https://doi.org/10.1007/s00245-018-9477-x

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