| 书目名称 | Lyapunov-type Inequalities | | 副标题 | With Applications to | | 编辑 | Juan Pablo Pinasco | | 视频video | | | 概述 | Emphasizes the use of Lyapunov-type inequalities to obtain lower bounds for eigenvalues.Devoted to more general nonlinear equations, systems of differential equations, or partial differential equation | | 丛书名称 | SpringerBriefs in Mathematics | | 图书封面 |  | | 描述 | 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 differ | | 出版日期 | Book 2013 | | 关键词 | Lyapunov inequality; Orlicz spaces; eigenvalue bounds; integral inequalities; p-laplace operator; quasili | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4614-8523-0 | | isbn_softcover | 978-1-4614-8522-3 | | isbn_ebook | 978-1-4614-8523-0Series ISSN 2191-8198 Series E-ISSN 2191-8201 | | issn_series | 2191-8198 | | copyright | Juan Pablo Pinasco 2013 |
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发表于 2025-3-21 17:06:06
