Asymptotically periodic solutions of neutral partial  differentialequations with infinite delay

Hernán R. Henríquez; Claudio Cuevas; Alejandro Caicedo

doi:10.3934/cpaa.2013.12.2031

Article Contents

2013, Volume 12, Issue 5: 2031-2068. Doi: 10.3934/cpaa.2013.12.2031

This issue Previous Article Existence and exponential decay for a nonlinear wave equation with nonlocal boundary conditions Next Article Distributional chaos for strongly continuous semigroups of operators

Asymptotically periodic solutions of neutral partial differential equations with infinite delay

1.
Departamento de Matemática, Universidad de Santiago, USACH, Casilla 307, Correo 2, Santiago
2.
Departamento de Matemática, Centro de Ciências Exatas e da Natureza, Universidade Federal de Pernambuco, Av. Jornalista Anibal Fernandes S/N, Cidade Universitária, CEP 50740-560, Recife-PE

Received: January 31, 2012

Revised: August 31, 2012

Published: August 2013

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Abstract

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.

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Mathematics Subject Classification: 34K05; 34A12; 34A40.

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