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.
Biography
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
V. V. Obukhovskii, G. Petrosyan, M. Soroka, “On an Initial Value Problem for Nonconvex-Valued Fractional Differential
Inclusions in a Banach Space”, Mat. Zametki, 115:3 (2024), 392–407; Math. Notes, 115:3 (2024), 358–370
2023
2.
M. I. Kamenskii, V. V. Obukhovskii, G. Petrosyan, “On Almost Periodic Trajectories of Control Systems with Feedback in the Form of Sweeping Processes”, Mat. Zametki, 114:1 (2023), 104–112; Math. Notes, 114:1 (2023), 85–91
2021
3.
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. Sovrem. Mat. Pril. Temat. Obz., 194 (2021), 38–45
4.
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, no. 5, 64–77; Russian Math. (Iz. VUZ), 65:5 (2021), 48–59
5.
V. V. Obukhovskii, M. M. Kulmanakova, M. M. Borovikova, “The solvability problem for a controlled system with a fractional derivative and a causal operator”, Taurida Journal of Computer Science Theory and Mathematics, 2021, no. 4, 85–105
6.
M. I. Kamenskii, V. V. Obukhovskii, G. Petrosyan, “On the existence of a solution for a periodic boundary value problem for semilinear fractional-order differential inclusions in Banach spaces”, Russian Universities Reports. Mathematics, 26:135 (2021), 250–270
7.
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
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
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. Sovrem. Mat. Pril. Temat. Obz., 186 (2020), 13–20
2019
10.
V. V. Obukhovskii, E. N. Getmanova, M. G. Karpov, “On random equilibrium points”, Russian Universities Reports. Mathematics, 24:125 (2019), 112–118
2018
11.
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
12.
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
13.
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
14.
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
2015
15.
B. D. Gel'man, V. V. Obukhovskii, “On fixed points of acyclic type multivalued maps”, Fundam. Prikl. Mat., 20:3 (2015), 47–59; J. Math. Sci., 225:4 (2017), 565–574
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, no. 5, 23–32; Russian Math. (Iz. VUZ), 53:5 (2009), 19–27
S. V. Kornev, V. V. Obukhovskii, “Non-smooth guiding potentials in problems on forced oscillations”, Avtomat. i Telemekh., 2007, no. 1, 3–10; Autom. Remote Control, 68:1 (2007), 1–8
M. M. Basova, V. V. Obukhovskii, “On some boundary-value problems for functional-differential inclusions in Banach spaces”, CMFD, 15 (2006), 36–44; Journal of Mathematical Sciences, 149:4 (2008), 1376–1384
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; Differ. Equ., 32:6 (1996), 755–762
Yu. G. Borisovich, V. V. Obukhovskii, “On an optimization problem for control systems of parabolic type”, Trudy Mat. Inst. Steklov., 211 (1995), 95–101; Proc. Steklov Inst. Math., 211 (1995), 85–91
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; J. Soviet Math., 64:2 (1993), 854–883
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; J. Soviet Math., 49:1 (1990), 800–855
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; J. Soviet Math., 39:3 (1987), 2772–2811
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; J. Soviet Math., 24:6 (1984), 719–791
V. V. Obukhovskii, A. G. Skaletskii, “Some theorems on the extension and quasiextension of continuous mappings”, Sibirsk. Mat. Zh., 23:4 (1982), 137–141; Siberian Math. J., 23:4 (1982), 556–559
1980
28.
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; Russian Math. Surveys, 35:1 (1980), 65–143
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
V. G. Zvyagin, V. V. Obukhovskii, “Yurii Grigor'evich Borisovich”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 5, 3–5
2008
32.
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; Russian Math. Surveys, 63:4 (2008), 767–769
2006
33.
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; Russian Math. Surveys, 61:5 (2006), 971–973
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
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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