TY  - BOOK
AU  - Berti,Massimiliano
ED  - SpringerLink (Online service)
TI  - Nonlinear Oscillations of Hamiltonian PDEs
T2  - Progress in Nonlinear Differential Equations and Their Applications,
SN  - 9780817646813
AV  - QA370-380 
U1  - 515.353 23
PY  - 2007///
CY  - Boston, MA
PB  - Birkhäuser Boston
KW  - Differential equations, partial
KW  - Differentiable dynamical systems
KW  - Mathematics
KW  - Number theory
KW  - Mathematical physics
KW  - Partial Differential Equations
KW  - Dynamical Systems and Ergodic Theory
KW  - Approximations and Expansions
KW  - Number Theory
KW  - Applications of Mathematics
KW  - Mathematical Methods in Physics
N1  - Finite Dimension -- Infinite Dimension -- A Tutorial in Nash–Moser Theory -- Application to the Nonlinear Wave Equation -- Forced Vibrations
N2  - 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
UR  - https://doi.org/10.1007/978-0-8176-4681-3
ER  -