  Selfdual variational calculus is further refined and used to address
questions of existence of local and global solutions for various parabolic
semi-linear equations, Hamiltonian systems of PDEs, as well as certain
nonlinear Schrodinger evolutions. This allows for the resolution of such
equations under general time boundary conditions which include the more
traditional ones such as initial value problems, periodic and anti-periodic
orbits, but also yield new ones such as "periodic orbits up to an isometry" for
evolution equations that may not have periodic solutions. In the process, we
introduce a method for perturbing selfdual functionals in order to induce
coercivity and compactness, while keeping the system selfdual.
