FAVARD THEORY AND FREDHOLM ALTERNATIVE FOR DISCONJUGATE RECURRENT SECOND ORDER EQUATIONS

摘要

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.