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2007, Volume 18, Issue 2&3: 271-293. Doi: 10.3934/dcds.2007.18.271
This issue Previous Article Existence and asymptotic behaviour for stochastic heat equations with multiplicative noise in materials with memory Next Article The exponential stability of neutral stochastic delay partial differential equations

Existence of exponentially attracting stationary solutions for delay evolution equations

  • 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

  • 3.

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

Received:  March 2006
Revised:  September 2006
Published:  June 2007
Abstract Related Papers Cited by
    Abstract
  • We consider the exponential stability of semilinear stochastic evolution equations with delays when zero is not a solution for these equations. We prove the existence of a non-trivial stationary solution exponentially stable, for which we use a general random fixed point theorem for general cocycles. We also construct stationary solutions with the stronger property of attracting bounded sets uniformly, by means of the theory of random dynamical systems and their conjugation properties.
    Mathematics Subject Classification: Primary: 60H15, 35K40.

    Citation:
    shu

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