Many partial differential equations (PDEs) that arise in physics can be viewed as infinite dimensional Hamiltonian systems. This monograph presents recent existence rsults of nonlinear oscillarions 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 center theorems, an analogous theory for completely resonant nonlinear wave equations is developed. Within this theory both problems of small divisors and infinite bifurcation phenomena occur, requiring the use of Nash-moser theory as well as minimax variational methods. These techinques are presented in a self contained manner toghether with other basic notions of Hamiltonian PDEs and number theory.

Nonlinear oscillations of Hamiltonian PDEs / Berti, Massimiliano. - 74:(2007), pp. 1-180. [10.1007/978-0-8176-4681-3]

Nonlinear oscillations of Hamiltonian PDEs

Berti, Massimiliano
2007-01-01

Abstract

Many partial differential equations (PDEs) that arise in physics can be viewed as infinite dimensional Hamiltonian systems. This monograph presents recent existence rsults of nonlinear oscillarions 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 center theorems, an analogous theory for completely resonant nonlinear wave equations is developed. Within this theory both problems of small divisors and infinite bifurcation phenomena occur, requiring the use of Nash-moser theory as well as minimax variational methods. These techinques are presented in a self contained manner toghether with other basic notions of Hamiltonian PDEs and number theory.
2007
1
180
https://www.springer.com/gp/book/9780817646806
Berti, Massimiliano
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/15718
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 24
  • ???jsp.display-item.citation.isi??? ND
social impact