Focal decompositions for linear differential equations of the second order (Q1773470)

Summary: Focal decomposition associated to an ordinary differential equation of second order is a partition of the set of all two-point boundary value problems according to the number of their solutions. Two equations are called focally equivalent if there exists a homomorphism of the set of two-point boundary value problems to itself such that the image of the focal decomposition associated to the first equation is a focal decomposition associated to the second one. In this paper, we present a complete classification for linear second-order equations with respect to this equivalence relation.