Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

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

Pages: 51 - 77, Volume 34, Issue 1, January 2014      doi:10.3934/dcds.2014.34.51

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Tomás Caraballo - Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Apdo. de Correos 1160, 41080 Sevilla, Spain (email)
Francisco Morillas - Department d'Economia Aplicada, Facultat d'Economia, Universitat de València, Campus del Tarongers s/n, 46022-València, Spain (email)
José Valero - Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, Avda. de la Universidad, s/n, 03202 Elche, Spain (email)

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:  Lattice dynamical systems, differential equations with delay, set-valued dynamical systems, global attractor.
Mathematics Subject Classification:  34K05, 34K31, 35B40, 35B41, 35K55, 58C06, 35K40.

Received: November 2012;      Revised: January 2013;      Available Online: June 2013.