Some Problems In Nonlinear Spectral Theory
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Author | : Jürgen Appell |
Publisher | : Walter de Gruyter |
Total Pages | : 421 |
Release | : 2008-08-22 |
Genre | : Mathematics |
ISBN | : 3110199262 |
Download Nonlinear Spectral Theory Book in PDF, Epub and Kindle
In view of the eminent importance of spectral theory of linear operators in many fields of mathematics and physics, it is not surprising that various attempts have been made to define and study spectra also for nonlinear operators. This book provides a comprehensive and self-contained treatment of the theory, methods, and applications of nonlinear spectral theory. The first chapter briefly recalls the definition and properties of the spectrum and several subspectra for bounded linear operators. Then some numerical characteristics for nonlinear operators are introduced which are useful for describing those classes of operators for which there exists a spectral theory. Since spectral values are closely related to solvability results for operator equations, various conditions for the local or global invertibility of a nonlinear operator are collected in the third chapter. The following two chapters are concerned with spectra for certain classes of continuous, Lipschitz continuous, or differentiable operators. These spectra, however, simply adapt the corresponding definitions from the linear theory which somehow restricts their applicability. Other spectra which are defined in a completely different way, but seem to have useful applications, are defined and studied in the following four chapters. The remaining three chapters are more application-oriented and deal with nonlinear eigenvalue problems, numerical ranges, and selected applications to nonlinear problems. The only prerequisite for understanding this book is a modest background in functional analysis and operator theory. It is addressed to non-specialists who want to get an idea of the development of spectral theory for nonlinear operators in the last 30 years, as well as a glimpse of the diversity of the directions in which current research is moving.
Author | : R. Chiappinelli |
Publisher | : |
Total Pages | : |
Release | : 1986 |
Genre | : |
ISBN | : |
Download Some Problems in Nonlinear Spectral Theory Book in PDF, Epub and Kindle
Author | : Julian Lopez-Gomez |
Publisher | : CRC Press |
Total Pages | : 281 |
Release | : 2001-03-28 |
Genre | : Mathematics |
ISBN | : 1420035509 |
Download Spectral Theory and Nonlinear Functional Analysis Book in PDF, Epub and Kindle
This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure set of zeroes of a general class of nonlinear operators. Appealing to a broad audience, it contains many important contributions to linear algebra, linear functional analysis, nonlinear functional analysis, and topology. The author gives several applications of the abstract theory to reaction diffusion equations and systems. The results presented cover a thirty-year period and cut across a variety of mathematical fields.
Author | : Janusz Mierczynski |
Publisher | : CRC Press |
Total Pages | : 333 |
Release | : 2008-03-24 |
Genre | : Mathematics |
ISBN | : 1584888962 |
Download Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications Book in PDF, Epub and Kindle
Providing a basic tool for studying nonlinear problems, Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications focuses on the principal spectral theory for general time-dependent and random parabolic equations and systems. The text contains many new results and considers existing results from a fresh perspective.
Author | : John F. Menick |
Publisher | : |
Total Pages | : 84 |
Release | : 1973 |
Genre | : |
ISBN | : |
Download Constraints, Intermediate Operators, and Multi-parameter Problems in Nonlinear Spectral Theory Book in PDF, Epub and Kindle
Author | : M. S. Birman |
Publisher | : American Mathematical Soc. |
Total Pages | : 268 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 9780821890745 |
Download Nonlinear Equations and Spectral Theory Book in PDF, Epub and Kindle
Translations of articles on mathematics appearing in various Russian mathematical serials.
Author | : Santiago Cano-casanova |
Publisher | : World Scientific |
Total Pages | : 289 |
Release | : 2005-09-29 |
Genre | : Science |
ISBN | : 9814479268 |
Download Spectral Theory And Nonlinear Analysis With Applications To Spatial Ecology Book in PDF, Epub and Kindle
This volume details some of the latest advances in spectral theory and nonlinear analysis through various cutting-edge theories on algebraic multiplicities, global bifurcation theory, non-linear Schrödinger equations, non-linear boundary value problems, large solutions, metasolutions, dynamical systems, and applications to spatial ecology.The main scope of the book is bringing together a series of topics that have evolved separately during the last decades around the common denominator of spectral theory and nonlinear analysis — from the most abstract developments up to the most concrete applications to population dynamics and socio-biology — in an effort to fill the existing gaps between these fields.
Author | : V. A. Yurko |
Publisher | : VSP |
Total Pages | : 324 |
Release | : 2002-01-01 |
Genre | : Mathematics |
ISBN | : 9789067643559 |
Download Method of Spectral Mappings in the Inverse Problem Theory Book in PDF, Epub and Kindle
Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics, mechanics, physics, electronics, geophysics, meteorology and other branches of natural science. This monograph deals with inverse problems of spectral analysis for ordinary differential equations and aims to present the main results on inverse spectral problems using the so-called method of spectral mappings, which is one of the main tools in inverse spectral theory.The book consists of three chapters and opens with the method of spectral mappings, presented in the simplest version for the Sturm-Liouville operator. The second chapter deals with the inverse problem of recovering higher-order differential operators of the form, on the half-line and on a finite interval. In this chapter the author introduces the so-called Weyl matrix, which is a generalization of the classical Weyl function for the selfadjoint second-order differential operator. The last chapter contains a study on inverse spectral problems for differential equations with nonlinear dependence on the spectral parameter.This monograph will be of value and interest to specialists in the field of inverse problems for differential equations.
Author | : Sergio Albeverio |
Publisher | : Birkhäuser |
Total Pages | : 444 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034880731 |
Download Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations Book in PDF, Epub and Kindle
This volume focuses on recent developments in non-linear and hyperbolic equations. It will be a most valuable resource for researchers in applied mathematics, the theory of wavelets, and in mathematical and theoretical physics. Nine up-to-date contributions have been written on invitation by experts in the respective fields. The book is the third volume of the subseries "Advances in Partial Differential Equations".
Author | : William Arveson |
Publisher | : |
Total Pages | : 290 |
Release | : 1979 |
Genre | : Nonlinear theories |
ISBN | : |
Download Nonlinear Spectral Theory, with Applications to Nonlinear Noise Book in PDF, Epub and Kindle