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:
    non sort: A
    title: Variational Approach to Lyapunov Type Inequalities
    sub title: From ODEs to PDEs
  name:
    name part: Cañada, Antonio.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Villegas, Salvador.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2015
    edition: 1st ed. 2015.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVIII, 120 p. online resource.
  abstract: This book highlights the current state of Lyapunov-type inequalities through a detailed analysis. Aimed toward researchers and students working in differential equations and those interested in the applications of stability theory and resonant systems, the book begins with an overview Lyapunov’s original results and moves forward to include prevalent results obtained in the past ten years. Detailed proofs and an emphasis on basic ideas are provided for different boundary conditions for ordinary differential equations, including Neumann, Dirichlet, periodic, and antiperiodic conditions. Novel results of higher eigenvalues, systems of equations, partial differential equations as well as variational approaches are presented. To this respect, a new and unified variational point of view is introduced for the treatment of such problems and a systematic discussion of different types of boundary conditions is featured. Various problems make the study of Lyapunov-type inequalities of interest to those in pure and applied mathematics. Originating with the study of the stability properties of the Hill equation, other questions arose for instance in systems at resonance, crystallography, isoperimetric problems, Rayleigh type quotients and oscillation and intervals of disconjugacy and it lead to the study of Lyapunov-type inequalities for differential equations. This classical area of mathematics is still of great interest and remains a source of inspiration. .
  table of contents: 1. Introduction -- 2. A variational characterization of the best Lyapunov constants -- 3. Higher eigenvalues -- 4. Partial differential equations -- 5. Systems of equations -- Index.
  note: by Antonio Cañada, Salvador Villegas.
  subject:
    topic: Mathematics
  subject:
    topic: Difference equations
  subject:
    topic: Functional equations
  subject:
    topic: Integral transforms
  subject:
    topic: Operational calculus
  subject:
    topic: Differential equations
  subject:
    topic: Partial differential equations
  subject:
    topic: Mathematics
  subject:
    topic: Ordinary Differential Equations
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Difference and Functional Equations
  subject:
    topic: Integral Transforms, Operational Calculus
  classification: QA372
  classification: 515.352
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: SpringerBriefs in Mathematics
  identifier: 9783319252896
  identifier: http://dx.doi.org/10.1007/978-3-319-25289-6
  record info:
    record creation date: 151124
    record change date: 20151124215930.0
    record identifier: 978-3-319-25289-6