ENGLISH

Nonlinear Oscillations of Hamiltonian PDEs

By Massimiliano Berti (auth.)

Book information

Publisher
Birkhäuser Basel
Year
2007
ISBN
0817646809, 9780817646806, 9780817646813
DOI
10.1007/978-0-8176-4681-3
Open Library ID
OL21412066M
Language
english
Format
PDF
Filesize
1 MB (1378220 bytes)
Series
Progress in Nonlinear Differential Equations and Their Applications 74
Edition
1
Pages
180\191
Library
Kolxo3
Time added
2009-07-20 03:45:11
Partial Differential Equations; Dynamical Systems

Description

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 resonant center theorems, the author develops the analogous theory for completely resonant nonlinear wave equations. 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 techniques are presented in a self-contained manner together with other basic notions of Hamiltonian PDEs and number theory. This text serves as an introduction to research in this fascinating and rapidly growing field. Graduate students and researchers interested in nonlinear variational techniques as well in small divisors problems applied to Hamiltonian PDEs will find inspiration in the book.

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