NCU FMCS NCU Polish version

Topological nonlinear analysis.

Applications of the Brouwer degree, Leray-Schauder degree and the Conley index to the study of solutions of abstract nonlinear problems.

Equivariant variational and topological methods.

Applications of

  • the degree for equivariant gradient maps,
  • the equivariant Morse theory,
  • the equivariant Conley index,
to the study of critical orbits of abstract nonlinear problems with variational structure.

Sufficient conditions for the existence, continuation, global bifurcation and symmetry breaking of critical orbits of invariant functionals. Development of the degree for equivariant gradient maps and its relations to the equivariant Conley index and the equivariant Morse theory. Classification of equivariant admissible gradient maps.

Differential equations of mathematical physics and mechanics.

Problems of existence, continuation, global bifurcation and symmetry breaking of

  • solutions of systems of elliptic differential equations with Dirichlet and Neumann boundary conditions,
  • periodic solutions of wave equations,
  • periodic solutions of Hamiltonian and Newtonian systems.

Hamiltonian systems with resonance at degenerate stationary solutions and at infinity.

Celestial mechanics.

The N-body problem. The restricted N-body problem. Problems of the existence, continuation, global bifurcations and symmetry breaking of periodic, homoclinic and heteroclinic solutions of Hamiltonian systems of celestial mechanics. Connected sets of solutions.

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