Existence of exponentially attracting stationary solutions for delay evolution equations. (English) Zbl 1125.60058

Summary: 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 exponentially stable solution, 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.


60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35K40 Second-order parabolic systems
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