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).
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
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
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