scholarly journals Long term dynamics of second order-in-time stochastic evolution equations with state-dependent delay

2018 ◽  
Vol 23 (3) ◽  
pp. 991-1009
Author(s):  
Igor Chueshov ◽  
◽  
Peter E. Kloeden ◽  
Meihua Yang ◽  
Keyword(s):  
Evolution Equations ◽  
Second Order ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Second Order In Time

scholarly journals Existence and Uniqueness of Solutions for Delay Stochastic Evolution Equations of Second Order in Time

2003 ◽  
Vol 03 (02) ◽  
pp. 141-167 ◽  
Author(s):  
María J. Garrido-Atienza ◽  
José Real
Keyword(s):  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Second Order ◽  
Point Of View ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Uniqueness Of Solutions ◽  
Second Order In Time ◽  
Functional Setting

Some results on the existence and uniqueness of solutions for stochastic evolution equations of second order in time, containing some hereditary characteristics, are proved. Our theory is developed from a variational point of view and in a general functional setting which permit us to deal with several kinds of delay terms in a unified formulation. The theory is illustrated with two examples.

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