Nonlinear Spectral Theory

Author : Jürgen Appell
Publisher : Walter de Gruyter
ISBN 13 : 3110199262
Total Pages : 421 pages
Book Rating : 4.60/5 ( download)

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Download or read book Nonlinear Spectral Theory written by Jürgen Appell and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Julian Lopez-Gomez
Publisher : CRC Press
ISBN 13 : 1420035509
Total Pages : 281 pages
Book Rating : 4.06/5 ( download)

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Download or read book Spectral Theory and Nonlinear Functional Analysis written by Julian Lopez-Gomez and published by CRC Press. This book was released on 2001-03-28 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :
Publisher :
ISBN 13 : 9814479268
Total Pages : pages
Book Rating : 4.64/5 ( download)

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Download or read book Spectral Theory and Nonlinear Analysis with Applications to Spatial Ecology written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : S. Fucik
Publisher : Springer
ISBN 13 : 3540378049
Total Pages : 290 pages
Book Rating : 4.44/5 ( download)

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Download or read book Spectral Analysis of Nonlinear Operators written by S. Fucik and published by Springer. This book was released on 2006-11-15 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : M. S. Birman
Publisher : American Mathematical Soc.
ISBN 13 : 9780821890745
Total Pages : 268 pages
Book Rating : 4.43/5 ( download)

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Download or read book Nonlinear Equations and Spectral Theory written by M. S. Birman and published by American Mathematical Soc.. This book was released on 2007 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Translations of articles on mathematics appearing in various Russian mathematical serials.

Author : Nabile Boussaïd
Publisher : American Mathematical Soc.
ISBN 13 : 1470443953
Total Pages : 297 pages
Book Rating : 4.55/5 ( download)

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Download or read book Nonlinear Dirac Equation: Spectral Stability of Solitary Waves written by Nabile Boussaïd and published by American Mathematical Soc.. This book was released on 2019-11-21 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Todd Kapitula
Publisher : Springer Science & Business Media
ISBN 13 : 1461469953
Total Pages : 369 pages
Book Rating : 4.57/5 ( download)

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Download or read book Spectral and Dynamical Stability of Nonlinear Waves written by Todd Kapitula and published by Springer Science & Business Media. This book was released on 2013-06-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Janusz Mierczynski
Publisher : CRC Press
ISBN 13 : 1584888962
Total Pages : 333 pages
Book Rating : 4.63/5 ( download)

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Download or read book Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications written by Janusz Mierczynski and published by CRC Press. This book was released on 2008-03-24 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Sergio Albeverio
Publisher : Birkhäuser
ISBN 13 : 3034880731
Total Pages : 444 pages
Book Rating : 4.32/5 ( download)

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Download or read book Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations written by Sergio Albeverio and published by Birkhäuser. This book was released on 2012-12-06 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : L.A. Sakhnovich
Publisher : Birkhäuser
ISBN 13 : 3034887132
Total Pages : 201 pages
Book Rating : 4.37/5 ( download)

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Download or read book Spectral Theory of Canonical Differential Systems. Method of Operator Identities written by L.A. Sakhnovich and published by Birkhäuser. This book was released on 2012-12-06 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theorems of factorising matrix functions and the operator identity method play an essential role in this book in constructing the spectral theory (direct and inverse problems) of canonical differential systems. Includes many varied applications of the general theory.