On differential equations with delay in Banach spaces and attractors forretarded lattice dynamical systems

Tomás Caraballo; Francisco Morillas; José Valero

doi:10.3934/dcds.2014.34.51

Article Contents

2014, Volume 34, Issue 1: 51-77. Doi: 10.3934/dcds.2014.34.51

This issue Previous Article On the convergence of statistical solutions of the 3D Navier-Stokes-$\alpha$ model as $\alpha$ vanishes Next Article Pathwise solutions of SPDEs driven by Hölder-continuous integrators with exponent larger than $1/2$ and random dynamical systems

On differential equations with delay in Banach spaces and attractors for retarded lattice dynamical systems

1.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Apdo. de Correos 1160, 41080 Sevilla
2.
Department d'Economia Aplicada, Facultat d'Economia, Universitat de València, Campus del Tarongers s/n, 46022-València
3.
Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, Avda. de la Universidad, s/n, 03202 Elche

Received: November 2012

Revised: January 2013

Published: January 2014

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Abstract

In this paper we first prove a rather general theorem about existence of solutions for an abstract differential equation in a Banach space by assuming that the nonlinear term is in some sense weakly continuous.
We then apply this result to a lattice dynamical system with delay, proving also the existence of a global compact attractor for such system.

Keywords:

Mathematics Subject Classification: 34K05, 34K31, 35B40, 35B41, 35K55, 58C06, 35K40.

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