Geodesic
On the index of the boundary value problem for a homogeneous Hamiltonian system of differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 3, pp. 490-497

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The index of the homogeneous self-adjoint boundary value problem for the Hamiltonian systems of ordinary differential equations is introduced. It is assumed that the system has a nontrivial solution. The relationship between the index of an eigenvalue of the nonlinear eigenvalue problem and the index of the corresponding homogeneous problem is established. Properties of the index of the problem and those of the eigenvalue are examined. 
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     title = {On the index of the boundary value problem for a~homogeneous {Hamiltonian} system of differential equations},
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A. A. Abramov; V. I. Ul'yanova; L. F. Yukhno. On the index of the boundary value problem for a homogeneous Hamiltonian system of differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 3, pp. 490-497. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_3_a8/