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September  2010, 14(2): 439-455. doi: 10.3934/dcdsb.2010.14.439

Asymptotic behaviour of a stochastic semilinear dissipative functional equation without uniqueness of solutions

Tomás Caraballo 1, , María J. Garrido–Atienza 1, , Björn Schmalfuss 2, and  José Valero 3,

1. 

Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain
2. 

Institut für Mathematik, Fakultät EIM, Universität Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany
3. 

Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, Avda. de la Universidad, s/n, 03202 Elche

Received  February 2009 Revised  July 2009 Published  June 2010

In this work we present the existence and uniqueness of pullback and random attractors for stochastic evolution equations with infinite delays when the uniqueness of solutions for these equations is not required. Our results are obtained by means of the theory of set-valued random dynamical systems and their conjugation properties.
Keywords: Multivalued non-autonomous and random dynamical systems, functional stochastic equations, conjugacy method., pullback and random attractors.
Mathematics Subject Classification: 60H15, 35K4.
Citation: Tomás Caraballo, María J. Garrido–Atienza, Björn Schmalfuss, José Valero. Asymptotic behaviour of a stochastic semilinear dissipative functional equation without uniqueness of solutions. Discrete and Continuous Dynamical Systems - Series B, 2010, 14 (2) : 439-455. doi: 10.3934/dcdsb.2010.14.439
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