Lyapunov-type inequalities : with applications to Eigenvalue problems

The Resource Lyapunov-type inequalities : with applications to Eigenvalue problems
Label
Lyapunov-type inequalities : with applications to Eigenvalue problems
Title remainder
with applications to Eigenvalue problems
Statement of responsibility
Juan Pablo Pinasco
Creator
Author
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 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
Member of
Cataloging source
GW5XE
Dewey number
515.352
Index
no index present
LC call number
QA871
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
SpringerBriefs in Mathematics,
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