Asymptotic behaviour of a stochastic semilinear dissipativefunctional equation without uniqueness of solutions

Tomás Caraballo; María J. Garrido–Atienza; Björn Schmalfuss; José Valero

doi:10.3934/dcdsb.2010.14.439

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2010, Volume 14, Issue 2: 439-455. Doi: 10.3934/dcdsb.2010.14.439

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

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

Received: January 31, 2009

Revised: June 30, 2009

Published: August 2010

Abstract Related Papers Cited by

Abstract

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,
pullback and random attractors,
functional stochastic equations,
conjugacy method.

Mathematics Subject Classification: 60H15, 35K40.

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