# American Institute of Mathematical Sciences

August  2016, 9(4): 959-977. doi: 10.3934/dcdss.2016036

## Recurrent equations with sign and Fredholm alternative

 1 Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada 2 Departamento de Matemática Aplicada, Universidad de Valladolid, Paseo del Cauce 59, 47011 Valladolid 3 Università di Milano, via Saldini 50, 20133 Milano, Italy

Received  July 2015 Revised  December 2015 Published  August 2016

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.
Citation: Juan Campos, Rafael Obaya, Massimo Tarallo. Recurrent equations with sign and Fredholm alternative. Discrete & Continuous Dynamical Systems - S, 2016, 9 (4) : 959-977. doi: 10.3934/dcdss.2016036
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##### References:
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