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Communications on Pure and Applied Analysis (CPAA)
 

Asymptotically periodic solutions of neutral partial differential equations with infinite delay

Pages: 2031 - 2068, Volume 12, Issue 5, September 2013      doi:10.3934/cpaa.2013.12.2031

 
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Hernán R. Henríquez - Departamento de Matemática, Universidad de Santiago, USACH, Casilla 307, Correo 2, Santiago, Chile (email)
Claudio Cuevas - 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, Brazil (email)
Alejandro Caicedo - 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, Brazil (email)

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.

Keywords:  Neutral functional differential equations, integro-differential equations, asymptotically almost automorphic functions, $S$-asymptotically $\omega$-periodic functions.
Mathematics Subject Classification:  34K05; 34A12; 34A40.

Received: February 2012;      Revised: September 2012;      Available Online: January 2013.

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