Geodesic
Nonlinear eigenvalue problem for a system of ordinary differential equations subject to a nonlocal condition
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 2, pp. 231-236

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For a system of linear ordinary differential equations supplemented with a nonlocal condition specified by the Stieltjes integral, the problem of calculating the eigenvalues belonging to a given bounded domain in the complex plane is examined. It is assumed that the coefficient matrix of the system and the matrix function in the Stieltjes integral are analytic functions of the spectral parameter. A numerically stable method for solving this problem is proposed and justified. It is based on the use of an auxiliary boundary value problem and formulas of the argument principle type. The problem of calculating the corresponding eigenfunctions is also treated. 
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     author = {A. A. Abramov and L. F. Yukhno},
     title = {Nonlinear eigenvalue problem for a system of ordinary differential equations subject to a nonlocal condition},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {231--236},
     publisher = {mathdoc},
     volume = {52},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_2_a6/}
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A. A. Abramov; L. F. Yukhno. Nonlinear eigenvalue problem for a system of ordinary differential equations subject to a nonlocal condition. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 2, pp. 231-236. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_2_a6/