Geodesic
Approximation of the bounded solution of an ordinary linear differential equation by solutions of two-point boundary-value problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 3, pp. 388-404

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The method of parametrization is used to obtain necessary and sufficient conditons for the correct solvability of the problem of finding the solution bounded on the entire real axis. For systems whose matrices and right-hand sides are constant in the limit, two-point bounary-value problems which approximate the problem in question are constructed. An estimate of the approximation is also given. The connection between the correct solvability of the original problem and that of the problem used as approximations is established. 
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     author = {D. S. Dzhumabaev},
     title = {Approximation of the bounded solution of an ordinary linear differential equation by solutions of two-point boundary-value problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     volume = {30},
     number = {3},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_3_a4/}
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D. S. Dzhumabaev. Approximation of the bounded solution of an ordinary linear differential equation by solutions of two-point boundary-value problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 3, pp. 388-404. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_3_a4/