Abstract and Applied Analysis
Volume 2003 (2003), Issue 14, Pages 813-821
doi:10.1155/S1085337503212057
Focal decompositions for linear differential equations of the second order
L. Birbrair1
, M. Sobolevsky2
and P. Sobolevskii3
1Departamento de Algebra, Geometria y Topologia, Universidad de Valladolid, Valladolid 47005, Spain
2Departamento de Matematica, Universidade Estadual do Ceará, Av. Paranjana, 1700, Fortaleza Cep. 60740-000, Brazil
3Institute of Mathematics, The Hebrew University, Givat Ram, Jerusalem 91904, Israel
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.