# American Institute of Mathematical Sciences

July  2017, 16(4): 1199-1232. doi: 10.3934/cpaa.2017059

## Favard theory and fredholm alternative for disconjugate recurrent second order equations

Received  June 2016 Revised  March 2017 Published  April 2017

Fund Project: This work was partially supported by MEC and FEDER MTM2014-53406-R, MTM2015-66330-P), Junta de Andalucía (FQM-954), MIUR (PRIN2012-201274FYK7) and EC (H2020-MSCA-ITN-2014)

We discuss the existence of a Fredholm–type Alternative for a recurrent second order linear equation, which is disconjugate in a strong sense. The basic result is about bounded solutions of equations with bounded coefficients: it depends on kinematic similarities that allow to reduce the problem to a pair of very simple normal forms. Then the result is specialized to recurrent equations, by means of Favard theory.

Citation: Juan Campos, Rafael Obaya, Massimo Tarallo. Favard theory and fredholm alternative for disconjugate recurrent second order equations. Communications on Pure & Applied Analysis, 2017, 16 (4) : 1199-1232. doi: 10.3934/cpaa.2017059
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