Floquet Theory for a Class of Periodic Evolution Equations in an Lp-Setting

In this work we explore the Floquet theory for evolution equations of the form u'(t)+At u(t)=0 (t real) where the operators At 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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