Favard theory and fredholm alternative for disconjugate recurrent second order equations

Juan Campos; Rafael Obaya; Massimo Tarallo

doi:10.3934/cpaa.2017059

Article Contents

2017, Volume 16, Issue 4: 1199-1232. Doi: 10.3934/cpaa.2017059

This issue Previous Article A critical exponent of Joseph-Lundgren type for an Hénon equation on the hyperbolic space Next Article Regularity of the global attractor for a nonlinear Schrödinger equation with a point defect

Favard theory and fredholm alternative for disconjugate recurrent second order equations

1.
Universidad de Granada, Campus Fuentenueva, 18071 Granada, Spain
2.
Universidad de Valladolid, Paseo del Cauce s/n, 47011 Valladolid, Spain
3.
Università di Milano, Via Saldini 50,20133 Milano, Italy

Received: May 31, 2016

Revised: February 28, 2017

Published: May 2017

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)

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Abstract

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.

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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