Linear elliptic and parabolic functional-differential equations with transformations of spatial variables in the regions of Euclidean space and their one-dimensional analogues.
Study of solvability, spectral properties and smoothness of generalized solutions and other qualitative properties of solutions of boundary value problems for elliptic functional-differential equations. Construction of the index theory. The study of solvability and smoothness of solutions of mixed problems for parabolic functional-differential equations.
Nonlocal elliptic problems, theory of multilayer plates and shells, nonlinear optical feedback systems, multidimensional diffusion processes, the Kato problem of the square root of the operator, variational problems for functionals with deviating arguments.