The Resource Lyapunov-type Inequalities : With Applications to Eigenvalue Problems, by Juan Pablo Pinasco, (electronic resource)

Lyapunov-type Inequalities : With Applications to Eigenvalue Problems, by Juan Pablo Pinasco, (electronic resource)

Label
Lyapunov-type Inequalities : With Applications to Eigenvalue Problems
Title
Lyapunov-type Inequalities
Title remainder
With Applications to Eigenvalue Problems
Statement of responsibility
by Juan Pablo Pinasco
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
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
Member of
http://library.link/vocab/creatorName
Pinasco, Juan Pablo
Image bit depth
0
LC call number
QA372
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
Series statement
SpringerBriefs in Mathematics,
http://library.link/vocab/subjectName
  • Mathematics
  • Functional equations
  • Differential Equations
  • Differential equations, partial
  • Mathematics
  • Ordinary Differential Equations
  • Several Complex Variables and Analytic Spaces
  • Difference and Functional Equations
Label
Lyapunov-type Inequalities : With Applications to Eigenvalue Problems, by Juan Pablo Pinasco, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Dimensions
unknown
Extent
XIII, 131 p.
File format
multiple file formats
Form of item
electronic
Isbn
9781461485230
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-1-4614-8523-0
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-1-4614-8523-0
Label
Lyapunov-type Inequalities : With Applications to Eigenvalue Problems, by Juan Pablo Pinasco, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Dimensions
unknown
Extent
XIII, 131 p.
File format
multiple file formats
Form of item
electronic
Isbn
9781461485230
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-1-4614-8523-0
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-1-4614-8523-0

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