000 03729nam a22005655i 4500
001 978-0-8176-4681-3
003 DE-He213
005 20181204132643.0
007 cr nn 008mamaa
008 100301s2007 xxu| s |||| 0|eng d
020 _a9780817646813
_9978-0-8176-4681-3
024 7 _a10.1007/978-0-8176-4681-3
_2doi
040 _aISI Library, Kolkata
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
082 0 4 _a515.353
_223
100 1 _aBerti, Massimiliano.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aNonlinear Oscillations of Hamiltonian PDEs
_h[electronic resource] /
_cby Massimiliano Berti.
264 1 _aBoston, MA :
_bBirkhäuser Boston,
_c2007.
300 _aXIV, 180 p. 10 illus.
_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,
_x1421-1750 ;
_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 _aDifferential equations, partial.
650 0 _aDifferentiable dynamical systems.
650 0 _aMathematics.
650 0 _aNumber theory.
650 0 _aMathematical physics.
650 1 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aDynamical Systems and Ergodic Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M1204X
650 2 4 _aApproximations and Expansions.
_0http://scigraph.springernature.com/things/product-market-codes/M12023
650 2 4 _aNumber Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M25001
650 2 4 _aApplications of Mathematics.
_0http://scigraph.springernature.com/things/product-market-codes/M13003
650 2 4 _aMathematical Methods in Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19013
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817671471
776 0 8 _iPrinted edition:
_z9780817646806
830 0 _aProgress in Nonlinear Differential Equations and Their Applications,
_x1421-1750 ;
_v74
856 4 0 _uhttps://doi.org/10.1007/978-0-8176-4681-3
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c425469
_d425469