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January  2014, 34(1): 51-77. doi: 10.3934/dcds.2014.34.51

## 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, Spain 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  June 2013

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.
Citation: Tomás Caraballo, Francisco Morillas, José Valero. On differential equations with delay in Banach spaces and attractors for retarded lattice dynamical systems. Discrete & Continuous Dynamical Systems - A, 2014, 34 (1) : 51-77. doi: 10.3934/dcds.2014.34.51
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