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

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
Asymptotically periodic solutions of neutral partial differential equations with infinite delay
Hernán R. Henríquez Claudio Cuevas Alejandro Caicedo
Communications on Pure & Applied Analysis 2013, 12(5): 2031-2068 doi: 10.3934/cpaa.2013.12.2031
In this paper we discuss the existence and uniqueness of asymptotically almost automorphic and $S$-asymptotically $\omega$-periodic mild solutions to some abstract nonlinear integro-differential equation of neutral type with infinite delay. We apply our results to neutral partial differential equations with infinite delay.
keywords: asymptotically almost automorphic functions Neutral functional differential equations integro-differential equations $S$-asymptotically $\omega$-periodic functions.

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