# American Institute of Mathematical Sciences

May  2017, 37(5): 2455-2482. doi: 10.3934/dcds.2017106

## Existence of solutions for a class of abstract neutral differential equations

 1 Departamento de Matemática, Universidad de Santiago, USACH, Casilla 307, correo 2, Santiago, Chile 2 Departamento de Matemática, Universidade Federal de Pernambuco, Recife-PE, CEP. 50540-740, Brazil 3 Instituto de Ciencias Físicas y Matemáticas, Facultad de Ciencias, Universidad Austral de Chile, Valdivia, Chile 4 Departamento de Matemática y Estadística, Universidad de La Frontera, Casilla 54-D, Temuco, Chile

* Corresponding author

1This author was partially supported by CONICYT under grant FONDECYT 1130144 and DICYT-USACH.
2This author was partially supported by CNPq/Brazil under Grant 478053/2013-4.
3This author was supported by CONICYT under grant FONDECYT Grant 3140103.
4This author was supported by project DIUFRO: DI17-0071.

Received  August 2014 Revised  January 2017 Published  February 2017

This paper is devoted to studying the existence of solutions for a general class of abstract neutral functional differential equations of first order with finite delay. Specifically, we distinguish among mild, strong and classical solutions, and we characterize in terms of the forcing function of the equation the existence of solutions of each one of these types.

Citation: Hernán R. Henríquez, Claudio Cuevas, Juan C. Pozo, Herme Soto. Existence of solutions for a class of abstract neutral differential equations. Discrete & Continuous Dynamical Systems, 2017, 37 (5) : 2455-2482. doi: 10.3934/dcds.2017106
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