EAN: 9783866445420

FLOQUET THEORY FOR A CLASS OF PERIODIC EVOLUTIO...

In this work we explore the Floquet theory for evolution equations of the form u'(t)+A_t u(t)=0
(t real) where the operators A_t periodically depend on t and the function u takes values in a
UMD Banach space X. We impose a suitable condition on the operator family (A_t) and their
common domain  in particular a decay condition for certain resolvents  to obtain the central
result that all exponentially bounded solutions can be described as a superposition of a fixed
family of Floquet solutions.

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