Obukhovskii, Valeri Vladimirovich

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Total publications: 30
Scientific articles: 26
Presentations: 1

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Obukhovskii, Valeri Vladimirovich
Doctor of physico-mathematical sciences (1993)
Speciality: 01.01.11 (System analisys)
Birth date: 27.04.1947
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. Yu. E. Bezmelnitsyna, S. V. Kornev, V. V. Obukhovskii, “Method of stochastic multivalent guiding functions in a periodic problem for stochastic differential inclusions”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 194 (2021),  38–45  mathnet
2. V. V. Obukhovskii, S. V. Kornev, E. N. Getmanova, “On the relative fixed point index for a class of noncompact multivalued maps”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, 5,  64–77  mathnet; Russian Math. (Iz. VUZ), 65:5 (2021), 48–59  isi  scopus
3. M. S. Afanasova, V. V. Obukhovskii, G. G. Petrosyan, “On a generalized boundary value problem for a feedback control system with infinite delay”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:2 (2021),  167–185  mathnet
4. V. V. Obukhovskii, S. V. Kornev, E. N. Getmanova, “On topological characteristics for some classes of multivalued mappings”, Chebyshevskii Sb., 21:2 (2020),  301–319  mathnet
5. Yu. E. Bezmelnitsyna, S. V. Kornev, V. V. Obukhovskii, “Nonsmooth integral direction potentials in the problem of the asymptotic behavior of trajectories of some classes of functional differential inclusions”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 186 (2020),  13–20  mathnet
6. V. V. Obukhovskii, E. N. Getmanova, M. G. Karpov, “On random equilibrium points”, Russian Universities Reports. Mathematics, 24:125 (2019),  112–118  mathnet  elib
7. S. V. Kornev, V. V. Obukhovskii, “Asymptotic behavior of solutions for inclusions with causal multioperators and the method of integral guiding potentials”, Tambov University Reports. Series: Natural and Technical Sciences, 23:122 (2018),  136–144  mathnet  elib
8. M. I. Kamenskii, V. V. Obukhovskii, G. Petrosyan, “On semidiscretization methods for differential inclusions of fractional order”, Tambov University Reports. Series: Natural and Technical Sciences, 23:122 (2018),  125–130  mathnet  elib
9. M. M. Kulmanakova, V. V. Obukhovskii, Y. L. Ul'yanova, “A generalized boundary value problem for a feedback control system with infinite delay”, Tambov University Reports. Series: Natural and Technical Sciences, 23:121 (2018),  44–64  mathnet  elib
10. S. V. Kornev, V. V. Obukhovskii, “Integral guiding potentials in the problem of asymptotic behavior of solutions for functional differential inclusions”, Tambov University Reports. Series: Natural and Technical Sciences, 23:121 (2018),  31–43  mathnet  elib
11. B. D. Gel'man, V. V. Obukhovskii, “On fixed points of acyclic type multivalued maps”, Fundam. Prikl. Mat., 20:3 (2015),  47–59  mathnet  mathscinet  elib; J. Math. Sci., 225:4 (2017), 565–574
12. S. V. Kornev, V. V. Obukhovskii, “Localization of the method of guiding functions in the problem about periodic solutions of differential inclusions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, 5,  23–32  mathnet  zmath; Russian Math. (Iz. VUZ), 53:5 (2009), 19–27
13. S. V. Kornev, V. V. Obukhovskii, “Non-smooth guiding potentials in problems on forced oscillations”, Avtomat. i Telemekh., 2007, 1,  3–10  mathnet  mathscinet  zmath; Autom. Remote Control, 68:1 (2007), 1–8  scopus
14. M. M. Basova, V. V. Obukhovskii, “On some boundary-value problems for functional-differential inclusions in Banach spaces”, CMFD, 15 (2006),  36–44  mathnet  mathscinet; Journal of Mathematical Sciences, 149:4 (2008), 1376–1384
15. A. G. Baskakov, V. V. Obukhovskii, P. Zecca, “On differential inclusions in uniform spaces of functions”, Izv. IMI UdGU, 2006, 3(37),  7–8  mathnet
16. S. V. Kornev, V. V. Obukhovskii, “On Nonsmooth Multivalent Guiding Functions”, Differ. Uravn., 39:11 (2003),  1497–1502  mathnet  mathscinet; Differ. Equ., 39:11 (2003), 1578–1584
17. M. I. Kamenskii, V. V. Obukhovskii, “On the operator of translation along the trajectories of semilinear controlled systems”, Differ. Uravn., 32:6 (1996),  747–754  mathnet  mathscinet; Differ. Equ., 32:6 (1996), 755–762
18. Yu. G. Borisovich, V. V. Obukhovskii, “On an optimization problem for control systems of parabolic type”, Trudy Mat. Inst. Steklov., 211 (1995),  95–101  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 211 (1995), 85–91
19. B. D. Gel'man, V. V. Obukhovskii, “New results in the theory of multivalued mappings. II. Analysis and applications”, Itogi Nauki i Tekhn. Ser. Mat. Anal., 29 (1991),  107–159  mathnet  mathscinet  zmath; J. Soviet Math., 64:2 (1993), 854–883
20. Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkis, V. V. Obukhovskii, “New results in the theory of multivalued mappings. I. Topological characteristics and solvability of operator relations”, Itogi Nauki i Tekhn. Ser. Mat. Anal., 25 (1987),  123–197  mathnet  mathscinet  zmath; J. Soviet Math., 49:1 (1990), 800–855
21. Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkis, V. V. Obukhovskii, “Multivalued analysis and operator inclusions”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 29 (1986),  151–211  mathnet  mathscinet  zmath; J. Soviet Math., 39:3 (1987), 2772–2811
22. Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkis, V. V. Obukhovskii, “Multivalued mappings”, Itogi Nauki i Tekhn. Ser. Mat. Anal., 19 (1982),  127–230  mathnet  mathscinet  zmath; J. Soviet Math., 24:6 (1984), 719–791
23. V. V. Obukhovskii, A. G. Skaletskii, “Some theorems on the extension and quasiextension of continuous mappings”, Sibirsk. Mat. Zh., 23:4 (1982),  137–141  mathnet  mathscinet  zmath; Siberian Math. J., 23:4 (1982), 556–559  isi
24. Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkis, V. V. Obukhovskii, “Topological methods in the fixed-point theory of multi-valued maps”, Uspekhi Mat. Nauk, 35:1(211) (1980),  59–126  mathnet  mathscinet  zmath; Russian Math. Surveys, 35:1 (1980), 65–143  isi
25. Ya. A. Izrailevich, V. V. Obukhovskii, “On equivariant multivalued mappings”, Dokl. Akad. Nauk SSSR, 205:1 (1972),  16–18  mathnet  mathscinet  zmath
26. Yu. G. Borisovich, B. D. Gel'man, È. Muhamadiev, V. V. Obukhovskii, “The rotation of multivalued vector fields”, Dokl. Akad. Nauk SSSR, 187:5 (1969),  971–973  mathnet  mathscinet  zmath

27. V. G. Zvyagin, V. V. Obukhovskii, “Yurii Grigor'evich Borisovich”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, 5,  3–5  mathnet
28. 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, “Yurii Grigor'evich Borisovich (obituary)”, Uspekhi Mat. Nauk, 63:4(382) (2008),  173–174  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 63:4 (2008), 767–769  isi
29. 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, “Kirill Andreevich Rodosskii (obituary)”, Uspekhi Mat. Nauk, 61:5(371) (2006),  173–175  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 61:5 (2006), 971–973  isi
30. Yu. G. Borisovich, B. D. Gel'man, È. M. Muhamadiev, V. V. Obukhovskii, “Поправки к статье “О вращении многозначных векторных полей” (ДАН, 187, № 5, 1969 г.)”, Dokl. Akad. Nauk SSSR, 190:6 (1970),  750  mathnet

Presentations in Math-Net.Ru
1. О степени совпадения для уплотняющего многозначного возмущения линейного фредгольмова оператора
Гетманова Екатерина Николаевна, С. В. Корнев, В. В. Обуховский
International Scientific Conference KOLMOGOROV READINGS – IX. General Control Problems and their Applications (GCP–2020), dedicated to the 70-th birth anniversary of Alexander Ivanovich Bulgakov and to the 90-th anniversary of the Institute of Mathematics, Physics and Information Technologies of Derzhavin Tambov State University
October 13, 2020 14:30   

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