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: Lyapunov-type Inequalities
    sub title: With Applications to Eigenvalue Problems
  name:
    name part: Pinasco, Juan Pablo.
    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: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 131 p. online resource.
  abstract: The eigenvalue problems for quasilinear and nonlinear operators present many differences with the linear case, and a Lyapunov inequality for quasilinear resonant systems showed the existence of eigenvalue asymptotics driven by the coupling of the equations instead of the order of the equations. For p=2, the coupling and the order of the equations are the same, so this cannot happen in linear problems. Another striking difference between linear and quasilinear second order differential operators is the existence of Lyapunov-type inequalities in R^n when p>n. Since the linear case corresponds to p=2, for the usual Laplacian there exists a Lyapunov inequality only for one-dimensional problems. For linear higher order problems, several Lyapunov-type inequalities were found by Egorov and Kondratiev and collected in On spectral theory of elliptic operators, Birkhauser Basel 1996. However, there exists an interesting interplay between the dimension of the underlying space, the order of the differential operator, the Sobolev space where the operator is defined, and the norm of the weight appearing in the inequality which is not fully developed. Also, the Lyapunov inequality for differential equations in Orlicz spaces can be used to develop an oscillation theory, bypassing the classical sturmian theory which is not known yet for those equations. For more general operators, like the p(x) laplacian, the possibility of existence of Lyapunov-type inequalities remains unexplored. .
  note: by Juan Pablo Pinasco.
  subject:
    topic: Mathematics
  subject:
    topic: Difference equations
  subject:
    topic: Functional equations
  subject:
    topic: Differential equations
  subject:
    topic: Functions of complex variables
  subject:
    topic: Mathematics
  subject:
    topic: Ordinary Differential Equations
  subject:
    topic: Several Complex Variables and Analytic Spaces
  subject:
    topic: Difference and Functional Equations
  classification: QA372
  classification: 515.352
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: SpringerBriefs in Mathematics
  identifier: 9781461485230
  identifier: http://dx.doi.org/10.1007/978-1-4614-8523-0
  record info:
    record creation date: 130914
    record change date: 20151030091557.0
    record identifier: 978-1-4614-8523-0