Periodic solutions for a class of nonlinear partial differential equations in higher dimension

contenuti We prove the existence of periodic solutions in a class of nonlinear partial differential equations, including the nonlinear Schr¨dinger equation, the nonlinear wave equation, and the nonlinear beam equation, in higher dimension. Our result covers cases of completely resonant equations, where the bifurcation equation is infinite-dimensional, such as the nonlinear Schr¨dinger equation with zero mass, for which solutions which at leading order are wave packets are shown to exist.