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.
Recurrent equations with sign and fredholm alternative / J. Campos, R. Obaya, M. Tarallo. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 9:4(2016 Aug), pp. 959-977. [10.3934/dcdss.2016036]
Recurrent equations with sign and fredholm alternative
M. TaralloUltimo
2016
Abstract
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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