000			03096nam a22005175i 4500
001			978-0-8176-4681-3
003			DE-He213
005			20251006084438.0
007			cr nn 008mamaa
008			100301s2007 xxu| s |||| 0|eng d
020			_a9780817646813
020			_a99780817646813
024	7		_a10.1007/978-0-8176-4681-3 _2doi
082	0	4	_a515.353 _223
100	1		_aBerti, Massimiliano. _eauthor.
245	1	0	_aNonlinear Oscillations of Hamiltonian PDEs _h[electronic resource] / _cby Massimiliano Berti.
264		1	_aBoston, MA : _bBirkhäuser Boston, _c2007.
300			_bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aProgress in Nonlinear Differential Equations and Their Applications ; _v74
505	0		_aFinite Dimension -- Infinite Dimension -- A Tutorial in Nash-Moser Theory -- Application to the Nonlinear Wave Equation -- Forced Vibrations.
520			_aMany 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.
650		0	_aMATHEMATICS.
650		0	_aDIFFERENTIABLE DYNAMICAL SYSTEMS.
650		0	_aDIFFERENTIAL EQUATIONS, PARTIAL.
650		0	_aNUMBER THEORY.
650		0	_aMATHEMATICAL PHYSICS.
650	1	4	_aMATHEMATICS.
650	2	4	_aPARTIAL DIFFERENTIAL EQUATIONS.
650	2	4	_aDYNAMICAL SYSTEMS AND ERGODIC THEORY.
650	2	4	_aAPPROXIMATIONS AND EXPANSIONS.
650	2	4	_aNUMBER THEORY.
650	2	4	_aAPPLICATIONS OF MATHEMATICS.
650	2	4	_aMATHEMATICAL METHODS IN PHYSICS.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817646806
830		0	_aProgress in Nonlinear Differential Equations and Their Applications ; _v74
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-4681-3 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59756 _d59756