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

Tomás Caraballo, María Garrido–Atienza, Björn Schmalfuss, José Valero
2010 Discrete and continuous dynamical systems. Series B  
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. 2000 Mathematics Subject Classification. 60H15, 35K40. Key words and phrases. Multivalued non-autonomous and random dynamical systems, pullback and random
more » ... d random attractors, functional stochastic equations, conjugacy method.
doi:10.3934/dcdsb.2010.14.439 fatcat:nackospk2jgttoanbq2mf53pxy