Recurrent equations with sign and Fredholm alternative

Juan Campos,Rafael Obaya,Massimo Tarallo

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S（2016）

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摘要

We prove that a Fredholm-type Alternative holds for recurrent equations with sign, extending a previous result by Cieutat and Haraux in [3]. Moreover, we show that this can be seen a particular case of [1] and we provide a solution to an interesting question raised by Hale in [6]. Finally we characterize the existence of exponential dichotomies also in the nonrecurrent case.

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关键词

Recurrent and almost periodic linear equations,bounded and recurrent solutions,spectral theory,Favard theory,Fredholm alternative

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