Geodesic
On a correctness of boundary value problems and continuous dependence of periodic solutions of controllable systems on parameters
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2010), pp. 11-21 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Conditions for continuous dependence on parameters of solution of a general boundary value problem are obtained for a functional-differential equation. The results are applied to investigation of a correctness of a linear general boundary value problem for the nonlinear differential equation with divergent argument and to problem of continuous dependence of periodic solutions of controllable system on control and divergence values.
Keywords: functional-differential equations, boundary value problems, continuous dependence of solutions on parameters, periodic solutions of controllable systems. 
@article{VUU_2010_1_a1,
     author = {E. O. Burlakov and E. S. Zhukovskii},
     title = {On a correctness of boundary value problems and continuous dependence of periodic solutions of controllable systems on parameters},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {11--21},
     year = {2010},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2010_1_a1/}
}
TY  - JOUR
AU  - E. O. Burlakov
AU  - E. S. Zhukovskii
TI  - On a correctness of boundary value problems and continuous dependence of periodic solutions of controllable systems on parameters
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2010
SP  - 11
EP  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VUU_2010_1_a1/
LA  - ru
ID  - VUU_2010_1_a1
ER  - 
%0 Journal Article
%A E. O. Burlakov
%A E. S. Zhukovskii
%T On a correctness of boundary value problems and continuous dependence of periodic solutions of controllable systems on parameters
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2010
%P 11-21
%N 1
%U http://geodesic.mathdoc.fr/item/VUU_2010_1_a1/
%G ru
%F VUU_2010_1_a1
E. O. Burlakov; E. S. Zhukovskii. On a correctness of boundary value problems and continuous dependence of periodic solutions of controllable systems on parameters. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2010), pp. 11-21. http://geodesic.mathdoc.fr/item/VUU_2010_1_a1/

[1] Maksimov V. P., Voprosy obschei teorii funktsionalno-differentsialnykh uravnenii, Izd-vo PGU, PSI, PSSGK, Perm, 2003, 306 pp.

[2] Vainiko G. M., “Regulyarnaya skhodimost operatorov i priblizhennoe reshenie uravnenii”, Itogi nauki i tekhniki. Matematicheskii analiz, no. 16, 1979, 5–53

[3] Artstein Z., “Continuous dependence of solutions of operator equations”, Trans. Amer. Math. Soc., 231:1 (1977), 143–166 | DOI | MR | Zbl

[4] Tonkov E. L., “Optimalnye periodicheskie dvizheniya upravlyaemoi sistemy”, Mat. fizika, 1977, no. 21, 45–59 | MR

[5] Tonkov E. L., “Optimalnoe upravlenie periodicheskimi dvizheniyami”, Mat. fizika, 1977, no. 22, 54–64 | MR | Zbl

[6] Krein S. G., Petunin Yu. I., Semenov E. M., Interpolyatsiya lineinykh operatorov, Nauka, M., 1978, 400 pp. | MR

[7] Krein S. G., Funktsionalnyi analiz, Nauka, M., 1972, 544 pp. | MR | Zbl

[8] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976, 544 pp. | MR

[9] Azbelev N. V., Maksimov V. P., Rakhmatullina L. F., Vvedenie v teoriyu funktsionalno-differentsialnykh uravnenii, Nauka, M., 1991, 280 pp. | MR | Zbl

[10] Zabreiko P. P., Koshelev A. I., Krasnoselskii M. A., Mikhlin S. G., Rakovschik L. S., Stetsenko V. Ya., Integralnye uravneniya, Nauka, M., 1968, 488 pp.