scholarly journals New criteria for the existence of periodic and almost periodic solutions for some evolution equations in Banach spaces

2004 ◽  
pp. 1-12 ◽  
Author(s):  
Khalil Ezzinbi ◽  
Mustapha Jazar
Keyword(s):  
Periodic Solutions ◽  
Banach Spaces ◽  
Evolution Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
New Criteria

ALMOST PERIODIC SOLUTIONS TO STOCHASTIC EVOLUTION EQUATIONS ON BANACH SPACES

2013 ◽  
Vol 13 (03) ◽  
pp. 1250027 ◽  
Author(s):  
P. CREWE
Keyword(s):  
Banach Space ◽  
Periodic Solutions ◽  
Banach Spaces ◽  
Evolution Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Stochastic Integration ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Semigroup Generator

We prove the existence of almost periodic solutions to a class of abstract stochastic evolution equations on a Banach space E, [Formula: see text] Both autonomous (A is a C0-semigroup generator) and non-autonomous (A(t) satisfies conditions of Acquistapace–Terreni and generates a strongly continuous evolution family) cases are studied. Results are based on the theory of stochastic integration on Banach spaces of van Neerven and Weis and R-boundedness estimates for semigroups and evolution families due to Hytönen and Veraar. An example is given for a non-autonomous second order boundary value problem on a domain in ℝd.

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