Abstract and Applied Analysis

Focal decompositions for linear differential equations of the second order

L. Birbrair, M. Sobolevsky, and P. Sobolevskii

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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.

Article information

Abstr. Appl. Anal., Volume 2003, Number 14 (2003), 813-821.

First available in Project Euclid: 15 September 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34A26: Geometric methods in differential equations


Birbrair, L.; Sobolevsky, M.; Sobolevskii, P. Focal decompositions for linear differential equations of the second order. Abstr. Appl. Anal. 2003 (2003), no. 14, 813--821. doi:10.1155/S1085337503212057. https://projecteuclid.org/euclid.aaa/1063629031

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