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periodic equation, monodromy operator, spectrum of a function, spectral criterion. Abbreviated title: A Spectral Criterion for Almost Periodicity
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@MISC{Naito_periodicequation,,
author = {Toshiki Naito and Nguyen Van Minh and Jong Son Shin},
title = {periodic equation, monodromy operator, spectrum of a function, spectral criterion. Abbreviated title: A Spectral Criterion for Almost Periodicity},
year = {}
}
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Abstract
This paper is concerned with equations of the form: u ′ = A(t)u + f(t) , where A(t) is (unbounded) periodic linear operator and f is almost periodic. We extend a central result on the spectral criteria for almost periodicity of solutions of evolution equations to some classes of periodic equations which says that if u is a bounded uniformly continuous mild solution and P is the monodromy operator, then their spectra satisfy eispAP (u) ⊂ σ(P) ∩ S1, where S1 is the unit circle. This result is then applied to find almost periodic solutions to the above-mentioned equations. In particular, parabolic and functional differential equations are considered. Existence conditions for almost periodic and quasi-periodic solutions are discussed.
Keyphrases
spectral criterion periodic equation monodromy operator abbreviated title almost periodicity periodic linear operator central result above-mentioned equation quasi-periodic solution unit circle functional differential equation continuous mild solution existence condition periodic solution spectrum satisfy eispap evolution equation
