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Second Order Abstract Neutral Functional Differential Equations

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Abstract

In this paper we are concerned with a class of second order abstract neutral functional differential equations with finite delay in a Banach space. We establish the existence of mild and classical solutions for the nonlinear equation, and we show that the map defined by the mild solutions of the linear equation is a strongly continuous semigroup of bounded linear operators on an appropriate space. We use this semigroup to establish a variation of constants formula to solve the inhomogeneous linear equation.

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Acknowledgments

The authors are very grateful to the anonymous reviewer for their dedicated work, which has allowed us to significantly improve the original manuscript. The first author was supported partially by CONICYT under Grant FONDECYT 1130144 and DICYT-USACH, and the second author was supported partially by CNPq/Brazil under Grant 478053/2013-4.

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Authors and Affiliations

  1. Departamento de Matemática, Universidad de Santiago, USACH, Casilla 307, Correo 2, Santiago, Chile

    Hernán R. Henríquez

  2. Departamento de Matemática, Universidade Federal de Pernambuco, Av. Prof. Luiz Freire S/N, Recife, PE, CEP 50540-740, Brazil

    Claudio Cuevas

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  1. Hernán R. Henríquez
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  2. Claudio Cuevas
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Correspondence to Hernán R. Henríquez.

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Henríquez, H.R., Cuevas, C. Second Order Abstract Neutral Functional Differential Equations. J Dyn Diff Equat 29, 615–653 (2017). https://doi.org/10.1007/s10884-015-9483-5

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  • DOI: https://doi.org/10.1007/s10884-015-9483-5

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