Obukhovskii Valeri Vladimirovich

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Total publications: 18
Scientific articles: 15

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Obukhovskii Valeri Vladimirovich
Doctor of physico-mathematical sciences (1993)
Speciality: 01.01.11 (System analisys)
Birth date: 27.04.1947
Phone: +7 (473) 255 36 63
Keywords: multivalued map; measure of noncompactness; condensing map; fixed point; topological degree; differential inclusion; control system; optimal solution.
UDC: 515.126.83, 517.988, 517.911.5, 517.977, 513.83, 517.927, 517.977.56
MSC: 34A60, 34G25, 34K05, 34K13, 34K30, 47H04, 47H09, 47H10, 47H11, 47J25, 49J24, 49K24, 54C60, 54C65, 55M20, 55M25


Main scientific interests lay in the sphere of contemporary multivalued analysis and its applications. The problems of solvability of nonlinear operator inclusions, of construction of the topological degree theory for various classes of noncompact multivalued maps, of description of topological structure of solutions sets were investigated. The applications of topological methods in the theory of differential inclusions were studied. In particular, for various classes of semilinear differential inclusions in a Banach space existence theorems for the Cauchy problem, the periodic problem, general boundary problems were obtained. Topological properties of solutions sets were investigated and applications to optimization problems for nonlinear control systems were given.


Graduated from the mathematical faculty of the Voronezh state University in 1970. Ph.D. thesis was defended in 1975 (Voronezh University) D.Sci. thesis was defended in 1993 (Institute of Control Problems of the RAS, Moscow) A list of my works contains more than 80 titles.

Fulbright grant for the work at the Rutgers University, USA (1994) Grant of the Italian Ministry of Foreign Affairs for the work at the University of Florence (1998) Grant of the Deutscher Akademischer Austauschdienst (DAAD) for the work at the Muenchen Technical University (2001) Soros Professor (1998–2001).

Main publications:
  • Kamenskii M., Obukhovskii V., Zecca P., Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, De Gruyter Series in Nonlinear Anal. and Appl. 7. Walter de Gruyter, Berlin - New York, 2001
List of publications on Google Scholar

Publications in Math-Net.Ru
1. On fixed points of acyclic type multivalued maps
B. D. Gel'man, V. V. Obukhovskii
Fundam. Prikl. Mat., 20:3 (2015),  47–59
2. Localization of the method of guiding functions in the problem about periodic solutions of differential inclusions
S. V. Kornev, V. V. Obukhovskii
Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 5,  23–32
3. Non-smooth guiding potentials in problems on forced oscillations
S. V. Kornev, V. V. Obukhovskii
Avtomat. i Telemekh., 2007, no. 1,  3–10
4. On some boundary-value problems for functional-differential inclusions in Banach spaces
M. M. Basova, V. V. Obukhovskii
CMFD, 15 (2006),  36–44
5. On differential inclusions in uniform spaces of functions
A. G. Baskakov, V. V. Obukhovskii, P. Zecca
Izv. IMI UdGU, 2006, no. 3(37),  7–8
6. On Nonsmooth Multivalent Guiding Functions
S. V. Kornev, V. V. Obukhovskii
Differ. Uravn., 39:11 (2003),  1497–1502
7. On the operator of translation along the trajectories of semilinear controlled systems
M. I. Kamenskii, V. V. Obukhovskii
Differ. Uravn., 32:6 (1996),  747–754
8. On an optimization problem for control systems of parabolic type
Yu. G. Borisovich, V. V. Obukhovskii
Trudy Mat. Inst. Steklov., 211 (1995),  95–101
9. New results in the theory of multivalued mappings. II. Analysis and applications
B. D. Gel'man, V. V. Obukhovskii
Itogi Nauki i Tekhn. Ser. Mat. Anal., 29 (1991),  107–159
10. New results in the theory of multivalued mappings. I. Topological characteristics and solvability of operator relations
Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkis, V. V. Obukhovskii
Itogi Nauki i Tekhn. Ser. Mat. Anal., 25 (1987),  123–197
11. Multivalued analysis and operator inclusions
Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkis, V. V. Obukhovskii
Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 29 (1986),  151–211
12. Multivalued mappings
Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkis, V. V. Obukhovskii
Itogi Nauki i Tekhn. Ser. Mat. Anal., 19 (1982),  127–230
13. Topological methods in the fixed-point theory of multi-valued maps
Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkis, V. V. Obukhovskii
Uspekhi Mat. Nauk, 35:1(211) (1980),  59–126
14. On equivariant multivalued mappings
Ya. A. Izrailevich, V. V. Obukhovskii
Dokl. Akad. Nauk SSSR, 205:1 (1972),  16–18
15. The rotation of multivalued vector fields
Yu. G. Borisovich, B. D. Gel'man, È. Muhamadiev, V. V. Obukhovskii
Dokl. Akad. Nauk SSSR, 187:5 (1969),  971–973

16. Yurii Grigor'evich Borisovich (obituary)
N. M. Bliznyakov, V. M. Buchstaber, Yu. E. Gliklikh, V. G. Zvyagin, A. S. Mishchenko, V. V. Obukhovskii, Yu. I. Sapronov, A. T. Fomenko, A. V. Chernavskii
Uspekhi Mat. Nauk, 63:4(382) (2008),  173–174
17. Kirill Andreevich Rodosskii (obituary)
R. A. Arhontova, A. G. Baskakov, I. A. Bakhtin, E. S. Belyaeva, Yu. G. Borisovich, A. S. Grechenko, V. R. Zachepa, A. A. Karatsuba, A. F. Kudinov, V. V. Obukhovskii, A. I. Perov, A. S. Potapov, E. M. Semenov, V. P. Trofimov, N. N. Udodenko
Uspekhi Mat. Nauk, 61:5(371) (2006),  173–175
18. Поправки к статье “О вращении многозначных векторных полей” (ДАН, 187, № 5, 1969 г.)
Yu. G. Borisovich, B. D. Gel'man, È. M. Muhamadiev, V. V. Obukhovskii
Dokl. Akad. Nauk SSSR, 190:6 (1970),  750

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