Existence of periodic, homoclinic and heteroclinic solutions of Hamiltonian systems.
Conley index and Morse theory in Banach spaces.
Connection between Conley index and topological degree in Banach spaces.
Bifurcations in von Karman equations.
Topological invariants of set-valued mappings and applications.
Conley index for set-valued flows in Hilbert spaces.
Seiberg-Witten invariants.
Topological and variational methods in solving second order PDEs.
Homoclinic div-grad type solutions. Orlicz-Sobolev spaces.
Homoclinic orbits for a class of Hamiltonian systems with almost periodic / bounded potential. Creating analytical tools (for example frames) used in approximation and estimation processes on manifolds (especially on sphere). In statistical research, in addition to typical estimation, there are ongoing research on the singularities of density functions and regression function on sphere. There exist first research on singular operators on sphere.
Module structure for E-cohomological Conleya index and applications in Hamiltonian equations. Degenerated and nondegenerated version of Arnolda conjecture 2n-dimensional torus.
