Elliptic and parabolic differential equations with nonlocal boundary conditions.
The study of different types of nonlocal boundary value problems for elliptic and parabolic differential equations, and their interrelation. Research of the solvability and qualitative properties of solutions. Construction of the index theory.
Elliptic and parabolic functional-differential equations, multidimensional diffusion processes, plasma theory, Vlasov kinetic equations.