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Libro

Lyapunov-type inequalities: with applications to eigenvalue problems

Pinasco, Juan PabloIcon
Fecha de publicación: 2013
Editorial: Springer
ISSN: 2191-8198
e-ISSN: 2191-8201
ISBN: 978-1-4614-8522-3
Idioma: Inglés
Clasificación temática:
Matemática Pura

Resumen

Introduction ​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. ​
Palabras clave: LYAPUNOV INEQUALITY , ORLICZ SPACES , EIGENVALUE BOUNDS , INTEGRAL INEQUALITIES , P-LAPLACE OPERATOR , QUASILINEAR OPERATORS
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info:eu-repo/semantics/closedAccess Excepto donde se diga explícitamente, este item se publica bajo la siguiente descripción: Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Unported (CC BY-NC-SA 2.5)
Identificadores
URI: http://hdl.handle.net/11336/135403
URL: https://link.springer.com/book/10.1007%2F978-1-4614-8523-0
DOI: https://doi.org/10.1007/978-1-4614-8523-0;
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Libros(IMAS)
Libros de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Pinasco, Juan Pablo; Lyapunov-type inequalities: with applications to eigenvalue problems; Springer; 1; 2013; 131
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