Geodesic
Approximation of bounded solutions and exponential dichotomy on the axis
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 11, pp. 1646-1660

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Lyapunov transformations possessing certain properties are used to construct regular two-point boundary-value problems as approximations to the problem of determining a bounded solution in the general case. The concept of "limiting solutions as $t\to\infty$" is defined and the behaviour of solutions of linear ordinary differential equations as $t\to\infty$ is investigated. The necessary and sufficient conditions are derived under which a singular boundary-value problem with conditions assigned at infinity is uniquely solvable, and an appropriate approximating problem is constructed. 
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     author = {D. S. Dzhumabaev},
     title = {Approximation of bounded solutions and exponential dichotomy on the axis},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1646--1660},
     publisher = {mathdoc},
     volume = {30},
     number = {11},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_11_a4/}
}
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D. S. Dzhumabaev. Approximation of bounded solutions and exponential dichotomy on the axis. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 11, pp. 1646-1660. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_11_a4/