Author: Guido Gentile and Michela Procesi
Title:
Periodic solutions for a class of nonlinear
partial differential equations in higher dimension
Abstract:
We prove the existence of periodic solutions in a class
of nonlinear partial differential equations, including
the nonlinear Schrödinger equation, the nonlinear wave equation,
and the nonlinear beam equation, in higher dimension.
Our result covers cases where the bifurcation equation
is infinite-dimensional, such as the nonlinear Schrödinger
equation with zero mass, for which solutions which at leading order
are wave packets are shown to exist.
Keywords: Nonlinear Schrödinger equation; Nonlinear wave equation; Nonlinear beam equation; Higher dimension PDEs; Completely resonant equations; Periodic solutions; Renormalisation Group; Tree formalism.
Guido Gentile
Dipartimento di Matematica
Università di Roma Tre
Largo San Leonardo Murialdo 1, 00146 Roma, Italy
e-mail: gentile@mat.uniroma3.it
Michela Procesi
Dipartimento di Matematica
Università di Napoli "Federico II"
Via Cinthia, 80126, Napoli, Italy.
e-mail: procesi@dma.unina.it