# American Institute of Mathematical Sciences

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2008, 21(2): 415-443. doi: 10.3934/dcds.2008.21.415

## Non--autonomous and random attractors for delay random semilinear equations without uniqueness

 1 Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla 2 Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080–Sevilla, Spain 3 Institut für Mathematik Fakultät EIM, Universität Paderborn, Warburger Strasse 100, 33098 Paderborn 4 Centro de Investigación Operativa, Universidad Miguel Hernández, Avda Universidad s/n, 03202 Elche, Alicante

Received  April 2007 Revised  November 2007 Published  March 2008

We first prove the existence and uniqueness of pullback and random attractors for abstract multi-valued non-autonomous and random dynamical systems. The standard assumption of compactness of these systems can be replaced by the assumption of asymptotic compactness. Then, we apply the abstract theory to handle a random reaction-diffusion equation with memory or delay terms which can be considered on the complete past defined by $\mathbb{R}^{-}$. In particular, we do not assume the uniqueness of solutions of these equations.
Citation: Tomás Caraballo, M. J. Garrido-Atienza, B. Schmalfuss, José Valero. Non--autonomous and random attractors for delay random semilinear equations without uniqueness. Discrete & Continuous Dynamical Systems - A, 2008, 21 (2) : 415-443. doi: 10.3934/dcds.2008.21.415
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