L. Birbrair, M. Sobolevsky, P. Sobolevskii, "Focal decompositions for linear differential equations of the second order", Abstract and Applied Analysis, vol. 2003, Article ID 141830, 9 pages, 2003. https://doi.org/10.1155/S1085337503212057
Focal decompositions for linear differential equations of the second order
Focal decomposition associated to an ordinary differential equation of the second order is a partition of the set of all two-points 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-points 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.
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