Lyapunov-type Inequalities

Name: Lyapunov-type Inequalities
Brand: Springer, Berlin
SKU: 9781461485223
Price: 217.76 PLN
Availability: InStock

With Applications to Eigenvalue Problems

Autor: Juan Pablo Pinasco

Język:

Oprawa: Miękka

Wydawca: Springer, Berlin

Dostępność: Dostępna u dostawcy

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217.76 zł

The eigenvalue problems for quasilinear and nonlinear operators present many differences with the li...

Informacje o książce

Autor

Juan Pablo Pinasco

Język

Angielski

Oprawa

Książka - Miękka

Data wydania

2013

strony

131

EAN

9781461485223

ISBN

1461485223

Enbook ID

01429120

Wydawca

Springer, Berlin

Waga

284

Wymiary

155 x 240 x 7

Pełny opis

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 pn. 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.

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Lyapunov-type Inequalities

With Applications to Eigenvalue Problems

Informacje o książce

Pełny opis

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