rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Nonlinear Oscillations of Hamiltonian PDEs
  name:
    name part: Berti, Massimiliano.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2007
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIV, 180 p. 10 illus. online resource.
  abstract: 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.
  table of contents: Finite Dimension -- Infinite Dimension -- A Tutorial in Nash–Moser Theory -- Application to the Nonlinear Wave Equation -- Forced Vibrations.
  note: by Massimiliano Berti.
  subject:
    topic: Mathematics
  subject:
    topic: Approximation theory
  subject:
    topic: Dynamics
  subject:
    topic: Ergodic theory
  subject:
    topic: Partial differential equations
  subject:
    topic: Applied mathematics
  subject:
    topic: Engineering mathematics
  subject:
    topic: Number theory
  subject:
    topic: Physics
  subject:
    topic: Mathematics
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Dynamical Systems and Ergodic Theory
  subject:
    topic: Approximations and Expansions
  subject:
    topic: Number Theory
  subject:
    topic: Applications of Mathematics
  subject:
    topic: Mathematical Methods in Physics
  classification: QA370-380
  classification: 515.353
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Progress in Nonlinear Differential Equations and Their Applications ; 74
  identifier: 9780817646813
  identifier: http://dx.doi.org/10.1007/978-0-8176-4681-3
  record info:
    record creation date: 100301
    record change date: 20151204143909.0
    record identifier: 978-0-8176-4681-3