Favard theory and fredholm alternative for disconjugate recurrent second order equations
Open Access
- 1 January 2017
- journal article
- research article
- Published by American Institute of Mathematical Sciences (AIMS) in Communications on Pure and Applied Analysis
- Vol. 16 (4) , 1199-1232
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
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