Bifurcation of free and forced vibrations for nonlinear wave and Kirchhoff equations via Nash-Moser theory

Nonlinear wave equations model the propagation of waves in a wide range of Nonlinear wave equations model the propagation of waves in a wide range of physical systems, from acoustics to electromagnetics, from seismic motions to vibrating string and elastic membranes, where oscillatory phenomena occur. Because of this intrinsic oscillatory physical structure, it is natural, from a mathematical point of view, to investigate the question of the existence of oscillations, namely periodic and quasi-periodic solutions, for the equations governing such physical systems. This is the central question of this Thesis.