Recurrent equations with sign and Fredholm alternative

Juan Campos; Rafael  Obaya; Massimo  Tarallo

doi:10.3934/dcdss.2016036

Article Contents

2016, Volume 9, Issue 4: 959-977. Doi: 10.3934/dcdss.2016036

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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

Received: June 30, 2015

Revised: November 30, 2015

Published: July 2016

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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.

Keywords:

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

Mathematics Subject Classification: Primary: 34C27; Secondary: 34B05, 34A30.

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References

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