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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] Dzhumabaev D. S., “Priznaki odnoznachnoi razreshimosti lineinoi kraevoi zadachi dlya obyknovennogo differentsialnogo uravneniya”, Zh. vychisl. matem. i matem. fiz., 29:1 (1989), 50–66 | MR | Zbl

[2] Dzhumabaev D. S., “Approksimatsiya ogranichennogo resheniya lineinogo obyknovennogo differentsialnogo uravneniya resheniyami dvukhtochechnykh kraevykh zadach”, Zh. vychisl. matem. i matem. fiz., 30:3 (1990), 388–404 | MR | Zbl

[3] Birger E. S., Lyalikova N. B., “O nakhozhdenii dlya nekotorykh sistem obyknovennykh differentsialnykh uravnenii reshenii s zadannym usloviem na beskonechnosti. I; II”, Zh. vychisl. matem. i matem. fiz., 5:6 (1965), 979–990 ; 6:3 (1966), 446–453 | MR | Zbl | MR | Zbl

[4] Abramov A. A., Balla K., Konyukhova N. B., “Perenos granichnykh uslovii iz osobykh tochek dlya sistem obyknovennykh differentsialnykh uravnenii”, Soobsch. po vychisl. matem., VTs AN SSSR, M., 1981 | MR

[5] Abramov A. A., Balla K., Konyukhova N. B., “Ustoichivye nachalnye mnogoobraziya i singulyarnye kraevye zadachi dlya sistem obyknovennykh differentsialnykh uravnenii”, Comput. Math. Banach Center Publs., 13, 1984, 319–351 | MR | Zbl

[6] Abramov A. A., Konyukhova H. B., “Perenos dopustimykh granichnykh uslovii iz osoboi tochki dlya sistem lineinykh obyknovennykh differentsialnykh uravnenii”, Soobsch. po prikl. matem., VTs AN SSSR, M., 1985 | MR

[7] Bylov B. F., Vinograd R. E., Grobman D. M., Nemytskii V. V., Teoriya pokazatelei Lyapunova i ee prilozheniya k voprosam ustoichivosti, Nauka, M., 1966 | MR | Zbl

[8] Daletskii Yu. L., Krein M. G., Ustoichivost reshenii differentsialnykh uravnenii v banakhovom prostranstve, Nauka, M., 1970 | MR

[9] Sansone Dzh., Obyknovennye differentsialnye uravneniya, v. II, Izd-vo inostr. lit., M., 1954