My research interest is in the theory of nonlinear partial differential equations. It is focussed on the fundamental questions of existence, non-existence, and structure of solution sets of nonlinear elliptic equations and inequalities. My recent research concentrates in the area known in the modern PDE literature as nonlinear Liouville type theorems. I am also interested in concentarion phenomena in nonlinear PDEs. Most recently I was working on nonlinear elliptic problems with nonlocal interactions, such as Choquard (or Schrödinger-Newton) type equations.
My earlier research was in the area of topological and variational methods of nonlinear analysis, in particular critical points theory, infinite dimensional Morse Theory and its applications to nonlinear elliptic equations and nonlinear problems associated with non-local operators.