Geodesic
Nonlinear eigenvalue problem for second-order Hamiltonian systems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 6, pp. 999-1002

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The nonlinear self-adjoint eigenvalue problem for a Hamiltonian system of two ordinary differential equations is examined under the assumption that the matrix of the system is a monotone function of the spectral parameter. Certain properties of eigenvalues that were previously established by the authors for Hamitonian systems of arbitrary order are now worked out in detail and made more precise for the above system. In particular, a single second-order ordinary differential equation is analyzed. 
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     author = {A. A. Abramov and V. I. Ul'yanova and L. F. Yukhno},
     title = {Nonlinear eigenvalue problem for second-order {Hamiltonian} systems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     number = {6},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a5/}
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A. A. Abramov; V. I. Ul'yanova; L. F. Yukhno. Nonlinear eigenvalue problem for second-order Hamiltonian systems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 6, pp. 999-1002. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a5/