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.
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
