Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems. This monograph presents recent existence results of nonlinear oscillations of Hamiltonian PDEs, particularly of periodic solutions for completely resonant nonlinear wave equations.

After introducing the reader to classical finite-dimensional dynamical system theory, including the Weinstein Moser and Fadell Rabinowitz bifurcation results, the author develops the analogous theory for nonlinear wave equations. The theory and applications of the Nash Moser theorem...