Selfdual Variational Principles for Periodic Solutions of Hamiltonian   and Other Dynamical Systems
  Selfdual variational principles are introduced in order to construct solutions for Hamiltonian and other dynamical systems which satisfy a variety of linear and nonlinear boundary conditions including many of the standard ones. These principles lead to new variational proofs of the existence of parabolic flows with prescribed initial conditions, as well as periodic, anti-periodic and skew-periodic orbits of Hamiltonian systems. They are based on the theory of anti-selfdual Lagrangians introduced and developed recently in [3], [4] and [5]. 
Nassif Ghoussoub and Abbas Moameni