Das Jacobowitz-Hartman Theorem. Ein Beweis mithilfe des Poincaré-Birkhoff Fixpunktsatzes

The Jacobowitz-Hartman Theorem makes a statement about solutions of certain periodic ordinary differential equations of second order, which are periodic in its variable of time. The theorem states, that such differential equations under some more assumptions have arbitrarily many likewise periodic solutions. Further, a bound can be declared, such that for each even integer above this bound there exists a solution of the differential equation with exactly this number of zeroes per period.

The theorem is proven in the present paper. The presented proof connects hamiltonian dynamical systems originating in physics, and a topological theorem in order to achieve this result.