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.
Favard theory and Fredholm Alternative for disconjugate recurrent second order equations / J. Campos, R. Obaya, M. Tarallo. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 16:4(2017 Jul), pp. 1199-1232. [10.3934/cpaa.2017059]
Favard theory and Fredholm Alternative for disconjugate recurrent second order equations
M. TaralloUltimo
2017
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.Pubblicazioni consigliate
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