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Existence of exponentially attracting stationary solutions for delay evolution equations

 

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Opened Access Existence of exponentially attracting stationary solutions for delay evolution equations
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Author: Caraballo Garrido, Tomás
Garrido Atienza, María José
Schmalfuss, Björn
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2007
Published in: Discrete and Continuous Dynamical Systems, 18(2-3), 271-293
Document type: Article
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.
Size: 278.8Kb
Format: PDF

URI: http://hdl.handle.net/11441/23663

DOI: http://dx.doi.org/10.3934/dcds.2007.18.271

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