02958nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020001800100020001900118024003500137082001600172100003400188245009600222264004600318300002100364336002600385337002600411338003600437347002400473490007800497505014600575520114200721650001701863650003801880650003701918650001901955650002601974650001702000650003602017650004202053650003502095650001902130650003302149650003702182710003402219773002002253776003602273830007802309856010102387978-0-8176-4681-3DE-He21320260521092030.0cr nn 008mamaa100301s2007    xxu|    s    |||| 0|eng d  a9780817646813  a997808176468137 a10.1007/978-0-8176-4681-32doi04a515.3532231 aBerti, Massimiliano.eauthor.10aNonlinear Oscillations of Hamiltonian PDEsh[electronic resource] /cby Massimiliano Berti. 1aBoston, MA :bBirkhäuser Boston,c2007.  bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aProgress in Nonlinear Differential Equations and Their Applications ;v740 aFinite Dimension -- Infinite Dimension -- A Tutorial in Nash-Moser Theory -- Application to the Nonlinear Wave Equation -- Forced Vibrations.  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. 0aMATHEMATICS. 0aDIFFERENTIABLE DYNAMICAL SYSTEMS. 0aDIFFERENTIAL EQUATIONS, PARTIAL. 0aNUMBER THEORY. 0aMATHEMATICAL PHYSICS.14aMATHEMATICS.24aPARTIAL DIFFERENTIAL EQUATIONS.24aDYNAMICAL SYSTEMS AND ERGODIC THEORY.24aAPPROXIMATIONS AND EXPANSIONS.24aNUMBER THEORY.24aAPPLICATIONS OF MATHEMATICS.24aMATHEMATICAL METHODS IN PHYSICS.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780817646806 0aProgress in Nonlinear Differential Equations and Their Applications ;v7440uhttp://dx.doi.org/10.1007/978-0-8176-4681-3zVer el texto completo en las instalaciones del CICY