Titlebook: Delay Equations; Functional-, Complex Odo Diekmann,Sjoerd M. Verduyn Lunel,Hanns-Otto Wa Book 1995 Springer Science+Business Media New York

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https://doi.org/10.1007/978-3-658-23727-1Floquet theory deals with periodic linear systems. Let a strongly continuous semigroup {.(.)}. on a complex Banach space . be given.

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Die Geschichte hinter diesem BuchLet a strongly continuous semigroup of operators {.(.)}. on a real Banach space . be given. Assume that . is ⊙-reflexive with respect to the semigroup. Consider a .-map G: .→.* on some open set . ? ..

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Unsere Hoffnungen haben sich nicht erfülltIn this section we use the prototype equation . with a smooth function .: ?→?, in order to illustrate basic results on the long-term behaviour of solutions and on the organization of the phase space. We assume that . satisfies the condition . for negative feedback and that/is bounded from above or from below.

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Linear RFDE as bounded perturbations,Consider the linear autonomous RFDE. where ζ denotes a . × . matrix-valued function whose entries belong to NBV. Alternatively we can write (see I.1.5)

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Spectral theory,In Chapter I we studied the large time behaviour of solutions of linear retarded functional differential equations. This study was based on the observation that for positive time, the solution .(·;.) of the RFDE . satisfies a renewal equation (I.2.10)

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Completeness or small solutions?,In Section 1.5 the large time behaviour of solutions of a linear retarded functional differential equation. was studied. Using the renewal equation and the inverse Laplace transform, we found the following representation [see (I.5.3)] for the solution of (1.1): . where

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