Geodesic
Topological degree of condensing multi-valued perturbations of the $(S)_+$-class maps and its applications
Contemporary Mathematics. Fundamental Directions, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 1, Tome 35 (2010), pp. 60-77.

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

Applications of topological characteristics of nonlinear (one-valued and multi-valued) maps are well-known efficient tools for the investigation of solvability for various problems of the theory of differential equations and of optimal control theory. In this paper, a construction of one such characteristic is proposed: this is the degree of condensing multi-valued perturbations of maps of class $(S)_+$. Principal properties of the characteristic are studied. The considered characteristic is applied for the investigation of a class of controllable systems. 
@article{CMFD_2010_35_a4,
     author = {V. G. Zvyagin and E. S. Baranovskii},
     title = {Topological degree of condensing multi-valued perturbations of the $(S)_+$-class maps and its applications},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {60--77},
     publisher = {mathdoc},
     volume = {35},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2010_35_a4/}
}
TY  - JOUR
AU  - V. G. Zvyagin
AU  - E. S. Baranovskii
TI  - Topological degree of condensing multi-valued perturbations of the $(S)_+$-class maps and its applications
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2010
SP  - 60
EP  - 77
VL  - 35
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2010_35_a4/
LA  - ru
ID  - CMFD_2010_35_a4
ER  - 
%0 Journal Article
%A V. G. Zvyagin
%A E. S. Baranovskii
%T Topological degree of condensing multi-valued perturbations of the $(S)_+$-class maps and its applications
%J Contemporary Mathematics. Fundamental Directions
%D 2010
%P 60-77
%V 35
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2010_35_a4/
%G ru
%F CMFD_2010_35_a4
V. G. Zvyagin; E. S. Baranovskii. Topological degree of condensing multi-valued perturbations of the $(S)_+$-class maps and its applications. Contemporary Mathematics. Fundamental Directions, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 1, Tome 35 (2010), pp. 60-77. http://geodesic.mathdoc.fr/item/CMFD_2010_35_a4/

[1] Baranovskii E. S., “Teorema o svyazi usloviya $\alpha$ i sobstvennosti otobrazheniya”, Trudy matematicheskogo fakulteta. Novaya seriya, 2006, no. 10, 15–17

[2] Baranovskii E. S., “O primenenii topologicheskoi stepeni k izucheniyu struktury mnozhestva reshenii odnogo klassa vklyuchenii”, Vestnik VGU. Seriya fizika, matematika, 2007, no. 1, 112–120

[3] Baranovskii E. S., Zvyagin V. G., “Konstruktsiya stepeni odnogo klassa mnogoznachnykh vozmuschenii operatorov, udovletvoryayuschikh usloviyu alfa”, Nelineinye granichnye zadachi, 16 (2006), 107–117

[4] Borisovich Yu. G., Gelman B. D., Myshkis A. D., Obukhovskii V. V., Vvedenie v teoriyu mnogoznachnykh otobrazhenii i differentsialnykh vklyuchenii, KomKniga, M., 2005 | MR

[5] Borsuk K., Teoriya retraktov, Mir, M., 1971 | MR

[6] Gelman B. D., “Topologicheskie svoistva mnozhestva nepodvizhnykh tochek mnogoznachnykh otobrazhenii”, Mat. sb., 188:12 (1997), 33–56 | MR | Zbl

[7] Dzekka P., Zvyagin V. G., Obukhovskii V. V., “Ob orientirovannom indekse sovpadenii dlya nelineinykh fredgolmovykh vklyuchenii”, Doklady RAN, 406:4 (2006), 443–446 | MR

[8] Zvyagin V. G., Dmitrienko V. T., “Gomotopicheskaya klassifikatsiya odnogo klassa nepreryvnykh otobrazhenii”, Matem. zametki, 31:5 (1982), 801–812 | MR | Zbl

[9] Krasnoselskii M. A., Zabreiko P. P., Geometricheskie metody nelineinogo analiza, Nauka, M., 1975 | MR

[10] Myshkis A. D., “Obobscheniya teoremy o tochke pokoya dinamicheskoi sistemy vnutri zamknutoi traektorii”, Mat. sb., 34(76):3 (1954), 525–540 | MR | Zbl

[11] Skrypnik I. V., Metody issledovaniya nelineinykh ellipticheskikh granichnykh zadach, Nauka, M., 1990 | MR | Zbl

[12] Gorniewicz L., Topological fixed point theory of multivalued mappings, Kluwer Academic Publishers, Dordrecht–Boston–London, 1999 | MR | Zbl

[13] Gorniewicz L., Granas A., Kryszewski W., “On the homotopy method in the fixed point index theory for multi-mappings of compact ANR's”, J. Math. Anal. Appl., 161:2 (1991), 457–473 | DOI | MR | Zbl

[14] Kamenskii M., Obukhovskii V., Zecca P., Condensing multivalued maps and semilinear differential inclusions in Banach spaces, Walter de Gruyter, Berlin–New York, 2001 | MR

[15] Obukhovskii V., Zecca P., Zvyagin V., “An oriented index for nonlinear Fredholm inclusions with nonconvex-valued perturbations”, Abstr. Appl. Anal., 2006 (2006), 1–21 | DOI | MR

[16] Zvyagin V. G., “On the theory of generalized condensing perturbations of continuous mappings”, Lecture Notes in Math., 1108, Springer, 1984, 173–193 | MR