Nonlinear Spectral Theory PDF Download
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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 | : 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
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 | : Everette Lee May |
Publisher | : |
Total Pages | : 140 |
Release | : 1971 |
Genre | : Nonlinear theories |
ISBN | : |
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Author | : S. Fucik |
Publisher | : Springer |
Total Pages | : 290 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540378049 |
Download Spectral Analysis of Nonlinear Operators 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 | : R. Chiappinelli |
Publisher | : |
Total Pages | : |
Release | : 1986 |
Genre | : |
ISBN | : |
Download Some Problems in Nonlinear Spectral Theory Book in PDF, ePub and Kindle
Author | : Todd Kapitula |
Publisher | : Springer Science & Business Media |
Total Pages | : 369 |
Release | : 2013-06-06 |
Genre | : Mathematics |
ISBN | : 1461469953 |
Download Spectral and Dynamical Stability of Nonlinear Waves Book in PDF, ePub and Kindle
This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory and application. The book isolates and methodically develops key ideas by working through illustrative examples that are subsequently synthesized into general principles. Many of the seminal examples of stability theory, including orbital stability of the KdV solitary wave, and asymptotic stability of viscous shocks for scalar conservation laws, are treated in a textbook fashion for the first time. It presents spectral theory from a dynamical systems and functional analytic point of view, including essential and absolute spectra, and develops general nonlinear stability results for dissipative and Hamiltonian systems. The structure of the linear eigenvalue problem for Hamiltonian systems is carefully developed, including the Krein signature and related stability indices. The Evans function for the detection of point spectra is carefully developed through a series of frameworks of increasing complexity. Applications of the Evans function to the Orientation index, edge bifurcations, and large domain limits are developed through illustrative examples. The book is intended for first or second year graduate students in mathematics, or those with equivalent mathematical maturity. It is highly illustrated and there are many exercises scattered throughout the text that highlight and emphasize the key concepts. Upon completion of the book, the reader will be in an excellent position to understand and contribute to current research in nonlinear stability.
Author | : Nabile Boussaïd |
Publisher | : American Mathematical Soc. |
Total Pages | : 297 |
Release | : 2019-11-21 |
Genre | : Education |
ISBN | : 1470443953 |
Download Nonlinear Dirac Equation: Spectral Stability of Solitary Waves Book in PDF, ePub and Kindle
This monograph gives a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. It turns out that the instability is not an intrinsic property of the Dirac equation that is only resolved in the framework of the second quantization with the Dirac sea hypothesis. Whereas general results about the Dirac-Maxwell and similar equations are not yet available, we can consider the Dirac equation with scalar self-interaction, the model first introduced in 1938. In this book we show that in particular cases solitary waves in this model may be spectrally stable (no linear instability). This result is the first step towards proving asymptotic stability of solitary waves. The book presents the necessary overview of the functional analysis, spectral theory, and the existence and linear stability of solitary waves of the nonlinear Schrödinger equation. It also presents the necessary tools such as the limiting absorption principle and the Carleman estimates in the form applicable to the Dirac operator, and proves the general form of the Dirac-Pauli theorem. All of these results are used to prove the spectral stability of weakly relativistic solitary wave solutions of the nonlinear Dirac equation.