Geodesic
Applications of covering mappings in the theory of implicit differential equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, Tome 165 (2019), pp. 21-33.

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is a brief review of results in the theory of covering mappings of metric spaces and vector metric spaces and its applications to implicit differential equations. For the Cauchy problem and boundary-value problems, we obtain existence conditions, estimates of solutions, and conditions of the continuous dependence of solutions on the parameters of the equation and initial and boundary conditions.
Keywords: covering mapping, map coincidence point, metric space, partially ordered space, implicit differential equation, Cauchy problem, boundary-value problem. 
@article{INTO_2019_165_a2,
     author = {E. O. Burlakov and T. V. Zhukovskaya and E. S. Zhukovskiy and N. P. Puchkov},
     title = {Applications of covering mappings in the theory of implicit differential equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {21--33},
     publisher = {mathdoc},
     volume = {165},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_165_a2/}
}
TY  - JOUR
AU  - E. O. Burlakov
AU  - T. V. Zhukovskaya
AU  - E. S. Zhukovskiy
AU  - N. P. Puchkov
TI  - Applications of covering mappings in the theory of implicit differential equations
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2019
SP  - 21
EP  - 33
VL  - 165
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2019_165_a2/
LA  - ru
ID  - INTO_2019_165_a2
ER  - 
%0 Journal Article
%A E. O. Burlakov
%A T. V. Zhukovskaya
%A E. S. Zhukovskiy
%A N. P. Puchkov
%T Applications of covering mappings in the theory of implicit differential equations
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2019
%P 21-33
%V 165
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2019_165_a2/
%G ru
%F INTO_2019_165_a2
E. O. Burlakov; T. V. Zhukovskaya; E. S. Zhukovskiy; N. P. Puchkov. Applications of covering mappings in the theory of implicit differential equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, Tome 165 (2019), pp. 21-33. http://geodesic.mathdoc.fr/item/INTO_2019_165_a2/

[1] Avakov E. R., Arutyunov A. V., Zhukovskii E. S., “Nakryvayuschie otobrazheniya i ikh prilozheniya k differentsialnym uravneniyam, ne razreshennym otnositelno proizvodnoi”, Differ. uravn., 45:5 (2009), 613–634 | MR | Zbl

[2] Arutyunov A. V., “Ustoichivost tochek sovpadeniya i mnogoznachnye nakryvayuschie otobrazheniya v metricheskikh prostranstvakh”, Dokl. RAN., 427:5 (2009), 583–585 | MR | Zbl

[3] Arutyunov A. V., “Iteratsionnyi metod nakhozhdeniya tochek sovpadeniya dvukh otobrazhenii”, Zh. vychisl. mat. mat. fiz., 52:11 (2012), 1947–1950 | MR | Zbl

[4] Arutyunov A. V., Zhukovskii E. S., Zhukovskii S. E., “O korrektnosti differentsialnykh uravnenii, ne razreshennykh otnositelno proizvodnoi”, Differ. uravn., 47:11 (2011), 1523–1537 | MR | Zbl

[5] Arutyunov A. V., Zhukovskii S. E., “Lokalnaya razreshimost upravlyaemykh sistem so smeshannymi ogranicheniyami”, Differ. uravn., 46:11 (2010), 1561–1570 | MR | Zbl

[6] Arutyunov A. V., Zhukovskii S. E., “Tochki sovpadeniya otobrazhenii v prostranstvakh s vektornoi metrikoi i ikh prilozheniya k differentsialnym uravneniyam i upravlyaemym sistemam”, Differ. uravn., 53:11 (2017), 1473–1481 | DOI | Zbl

[7] Borisovich Yu. G., Gelman B. D., Myshkis A. D., Obukhovskii V. V., Vvedenie v teoriyu mnogoznachnykh otobrazhenii i differentsialnykh vklyuchenii, Librokom, M., 2011

[8] Zhukovskii E. S., “O tochkakh sovpadeniya vektornykh otobrazhenii”, Izv. vuzov. Mat., 2016, no. 10, 14–28

[9] Zhukovskii E. S., “O vozmuscheniyakh vektorno nakryvayuschikh otobrazhenii i sistemakh uravnenii v metricheskikh prostranstvakh”, Sib. mat. zh., 57:2 (2016), 297–311 | MR | Zbl

[10] Zhukovskaya T. V., Zhukovskii E. S., “Ob iteratsionnykh metodakh resheniya uravnenii s nakryvayuschimi otobrazheniyami”, Sib. zh. vychisl. mat., 19:4 (2016), 357–369 | MR | Zbl

[11] Zhukovskii E. S., Pluzhnikova E. A., “Nakryvayuschie otobrazheniya v proizvedenii metricheskikh prostranstv i kraevye zadachi dlya differentsialnykh uravnenii, ne razreshennykh otnositelno proizvodnoi”, Differ. uravn., 49:4 (2013), 439–455 | Zbl

[12] Zhukovskii E. S., Treschev V. S., Nakryvayuschie otobrazheniya v teorii neyavnykh differentsialnykh uravnenii s otklonyayuschimsya argumentom, TGU im. G. R. Derzhavina, Tambov, 2016

[13] Arutyunov A., Avakov E., Gel'man B., Dmitruk A., Obukhovskii V., “Locally covering maps in metric spaces and coincidence points”, J. Fixed Point Theory Appl., 5:1 (2009), 105–127 | DOI | MR | Zbl

[14] Zhukovskiy S., “On covering properties in variational analysis and optimization”, Set-Valued Var. Anal., 23:3 (2015), 415–424 | DOI | MR | Zbl