Existence of solutions for a class of abstract neutral differential equations

Hernán R. Henríquez; Claudio Cuevas; Juan C. Pozo; Herme Soto

doi:10.3934/dcds.2017106

Article Contents

2017, Volume 37, Issue 5: 2455-2482. Doi: 10.3934/dcds.2017106

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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
* 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: July 31, 2014

Revised: December 31, 2016

Published: May 2017

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Abstract

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.

Keywords:

Neutral functional differential equations,
mild solutions,
strong solutions,
classical solutions,
abstract Cauchy problem,
semigroup of operators.

Mathematics Subject Classification: Primary: 34K40, 34K30; Secondary: 34G20.

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