Lyapunov-type inequalities with applications to Eigenvalue problems Juan Pablo Pinasco

Format:

Book

Author/Creator:

Pinasco, Juan Pablo, author.

Series:

SpringerBriefs in mathematics 2191-8198

SpringerBriefs in Mathematics 2191-8198

Language:

English

Subjects (All):

Lyapunov functions.

Physical Description:

1 online resource

Place of Publication:

New York, NY Springer 2013

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 Rn 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

Contents:

Introduction Lyapunov's Inequality Nehari-Calogero-Cohn Inequality Bargmann-Type Bounds Miscellaneous Topics

Notes:

Includes bibliographical references

Online resource; title from PDF title page (SpringerLink, viewed September 16, 2013)

Other Format:

Print version Pinasco, Juan Pablo. Lyapunov-type Inequalities : With Applications to Eigenvalue Problems

ISBN:

9781461485230

1461485231

1461485223

9781461485223

OCLC:

859400654

Access Restriction:

Restricted for use by site license