Abstract and Applied Analysis

Abstract and Applied Analysis / 2003 / Article

Open Access

Volume 2003 |Article ID 141830 | https://doi.org/10.1155/S1085337503212057

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

Received10 Nov 2002

Abstract

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.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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