Linear elliptic and parabolic functional-differential equations with transformations of spatial variables in the regions of Euclidean space and their one-dimensional analogues.
Elliptic and parabolic differential equations with nonlocal boundary conditions.
Mixed problems for quasi-linear parabolic functional-differential equations with transformations of spatial variables.
Research on the theory of operators and functional spaces cover problems of evaluations of norms of operators of classical analysis and their generalizations in various functional spaces: shared ideal and Banach function spaces, generalized Morrey, Sobolev-Morrie spaces, Orlicz-Lorentz spaces and others.
Research on spectral operator theory covers the problems of spectral stability of differential operators associated with boundary value problems in varying the domain of their definition, as well as the problems of convergence and summability of spectral expansions by eigenfunctions of differential operators, such as the Laplace operator in the multidimensional domain.
Mathematical models in Oncology, Immunology, for the cardiovascular system.