03096nam a22005175i 4500 978-0-8176-4681-3 DE-He213 20260521092030.0 cr nn 008mamaa 100301s2007 xxu| s |||| 0|eng d 9780817646813 99780817646813 10.1007/978-0-8176-4681-3 doi 515.353 23 Berti, Massimiliano. author. Nonlinear Oscillations of Hamiltonian PDEs [electronic resource] / by Massimiliano Berti. Boston, MA : Birkhäuser Boston, 2007. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Progress in Nonlinear Differential Equations and Their Applications ; 74 Finite Dimension -- Infinite Dimension -- A Tutorial in Nash-Moser Theory -- Application to the Nonlinear Wave Equation -- Forced Vibrations. 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. MATHEMATICS. DIFFERENTIABLE DYNAMICAL SYSTEMS. DIFFERENTIAL EQUATIONS, PARTIAL. NUMBER THEORY. MATHEMATICAL PHYSICS. MATHEMATICS. PARTIAL DIFFERENTIAL EQUATIONS. DYNAMICAL SYSTEMS AND ERGODIC THEORY. APPROXIMATIONS AND EXPANSIONS. NUMBER THEORY. APPLICATIONS OF MATHEMATICS. MATHEMATICAL METHODS IN PHYSICS. SpringerLink (Online service) Springer eBooks Printed edition: 9780817646806 Progress in Nonlinear Differential Equations and Their Applications ; 74 http://dx.doi.org/10.1007/978-0-8176-4681-3 Ver el texto completo en las instalaciones del CICY ZDB-2-SMA ddc ER 35689 35689 0 0 ddc 0 0 LE CICY CICY EL 2025-10-06 0 515.353 2025-10-06 08:44:38 2025-10-06 ER