Periodic Differential Operators

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Periodic Differential Operators

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Author : B. Malcolm Brown
Publisher : Springer Science & Business Media
ISBN 13 : 3034805284
Total Pages : 220 pages
Book Rating : 4.0/5 (348 download)

Book Synopsis Periodic Differential Operators by : B. Malcolm Brown

Download or read book Periodic Differential Operators written by B. Malcolm Brown and published by Springer Science & Business Media. This book was released on 2012-10-30 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Periodic differential operators have a rich mathematical theory as well as important physical applications. They have been the subject of intensive development for over a century and remain a fertile research area. This book lays out the theoretical foundations and then moves on to give a coherent account of more recent results, relating in particular to the eigenvalue and spectral theory of the Hill and Dirac equations. The book will be valuable to advanced students and academics both for general reference and as an introduction to active research topics.

Transmutation Operators and Mean-periodic Functions Associated with Differential Operators

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Author : K. Trimèche
Publisher : CRC Press
ISBN 13 : 9783718648221
Total Pages : 300 pages
Book Rating : 4.6/5 (482 download)

Book Synopsis Transmutation Operators and Mean-periodic Functions Associated with Differential Operators by : K. Trimèche

Download or read book Transmutation Operators and Mean-periodic Functions Associated with Differential Operators written by K. Trimèche and published by CRC Press. This book was released on 1988 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Periodic Integral and Pseudodifferential Equations with Numerical Approximation

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Author : Jukka Saranen
Publisher : Springer Science & Business Media
ISBN 13 : 3662047969
Total Pages : 461 pages
Book Rating : 4.6/5 (62 download)

Book Synopsis Periodic Integral and Pseudodifferential Equations with Numerical Approximation by : Jukka Saranen

Download or read book Periodic Integral and Pseudodifferential Equations with Numerical Approximation written by Jukka Saranen and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: An attractive book on the intersection of analysis and numerical analysis, deriving classical boundary integral equations arising from the potential theory and acoustics. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.

Stability & Periodic Solutions of Ordinary & Functional Differential Equations

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Author : T. A. Burton
Publisher : Courier Corporation
ISBN 13 : 0486150453
Total Pages : 352 pages
Book Rating : 4.4/5 (861 download)

Book Synopsis Stability & Periodic Solutions of Ordinary & Functional Differential Equations by : T. A. Burton

Download or read book Stability & Periodic Solutions of Ordinary & Functional Differential Equations written by T. A. Burton and published by Courier Corporation. This book was released on 2014-06-24 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book's discussion of a broad class of differential equations includes linear differential and integrodifferential equations, fixed-point theory, and the basic stability and periodicity theory for nonlinear ordinary and functional differential equations.

Almost Periodic Differential Equations

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Author : A.M. Fink
Publisher : Springer
ISBN 13 : 3540383077
Total Pages : 345 pages
Book Rating : 4.5/5 (43 download)

Book Synopsis Almost Periodic Differential Equations by : A.M. Fink

Download or read book Almost Periodic Differential Equations written by A.M. Fink and published by Springer. This book was released on 2006-11-15 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Spectral Theory of Periodic Differential Equations

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Author : Michael Stephen Patrick Eastham
Publisher :
ISBN 13 :
Total Pages : 148 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis The Spectral Theory of Periodic Differential Equations by : Michael Stephen Patrick Eastham

Download or read book The Spectral Theory of Periodic Differential Equations written by Michael Stephen Patrick Eastham and published by . This book was released on 1973 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Homogenization of Differential Operators and Integral Functionals

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Author : V.V. Jikov
Publisher : Springer Science & Business Media
ISBN 13 : 3642846599
Total Pages : 583 pages
Book Rating : 4.6/5 (428 download)

Book Synopsis Homogenization of Differential Operators and Integral Functionals by : V.V. Jikov

Download or read book Homogenization of Differential Operators and Integral Functionals written by V.V. Jikov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: It was mainly during the last two decades that the theory of homogenization or averaging of partial differential equations took shape as a distinct mathe matical discipline. This theory has a lot of important applications in mechanics of composite and perforated materials, filtration, disperse media, and in many other branches of physics, mechanics and modern technology. There is a vast literature on the subject. The term averaging has been usually associated with the methods of non linear mechanics and ordinary differential equations developed in the works of Poincare, Van Der Pol, Krylov, Bogoliubov, etc. For a long time, after the works of Maxwell and Rayleigh, homogeniza tion problems for· partial differential equations were being mostly considered by specialists in physics and mechanics, and were staying beyond the scope of mathematicians. A great deal of attention was given to the so called disperse media, which, in the simplest case, are two-phase media formed by the main homogeneous material containing small foreign particles (grains, inclusions). Such two-phase bodies, whose size is considerably larger than that of each sep arate inclusion, have been discovered to possess stable physical properties (such as heat transfer, electric conductivity, etc.) which differ from those of the con stituent phases. For this reason, the word homogenized, or effective, is used in relation to these characteristics. An enormous number of results, approximation formulas, and estimates have been obtained in connection with such problems as electromagnetic wave scattering on small particles, effective heat transfer in two-phase media, etc.

Spectral Theory of Ordinary Differential Operators

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Author : Joachim Weidmann
Publisher : Springer
ISBN 13 : 3540479120
Total Pages : 310 pages
Book Rating : 4.5/5 (44 download)

Book Synopsis Spectral Theory of Ordinary Differential Operators by : Joachim Weidmann

Download or read book Spectral Theory of Ordinary Differential Operators written by Joachim Weidmann and published by Springer. This book was released on 2006-11-15 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes will be useful and of interest to mathematicians and physicists active in research as well as for students with some knowledge of the abstract theory of operators in Hilbert spaces. They give a complete spectral theory for ordinary differential expressions of arbitrary order n operating on -valued functions existence and construction of self-adjoint realizations via boundary conditions, determination and study of general properties of the resolvent, spectral representation and spectral resolution. Special attention is paid to the question of separated boundary conditions, spectral multiplicity and absolutely continuous spectrum. For the case nm=2 (Sturm-Liouville operators and Dirac systems) the classical theory of Weyl-Titchmarch is included. Oscillation theory for Sturm-Liouville operators and Dirac systems is developed and applied to the study of the essential and absolutely continuous spectrum. The results are illustrated by the explicit solution of a number of particular problems including the spectral theory one partical Schrödinger and Dirac operators with spherically symmetric potentials. The methods of proof are functionally analytic wherever possible.

Floquet Theory for Partial Differential Equations

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Author : P.A. Kuchment
Publisher : Birkhäuser
ISBN 13 : 3034885733
Total Pages : 363 pages
Book Rating : 4.0/5 (348 download)

Book Synopsis Floquet Theory for Partial Differential Equations by : P.A. Kuchment

Download or read book Floquet Theory for Partial Differential Equations written by P.A. Kuchment and published by Birkhäuser. This book was released on 2012-12-06 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear differential equations with periodic coefficients constitute a well developed part of the theory of ordinary differential equations [17, 94, 156, 177, 178, 272, 389]. They arise in many physical and technical applications [177, 178, 272]. A new wave of interest in this subject has been stimulated during the last two decades by the development of the inverse scattering method for integration of nonlinear differential equations. This has led to significant progress in this traditional area [27, 71, 72, 111 119, 250, 276, 277, 284, 286, 287, 312, 313, 337, 349, 354, 392, 393, 403, 404]. At the same time, many theoretical and applied problems lead to periodic partial differential equations. We can mention, for instance, quantum mechanics [14, 18, 40, 54, 60, 91, 92, 107, 123, 157-160, 192, 193, 204, 315, 367, 412, 414, 415, 417], hydrodynamics [179, 180], elasticity theory [395], the theory of guided waves [87-89, 208, 300], homogenization theory [29, 41, 348], direct and inverse scattering [175, 206, 216, 314, 388, 406-408], parametric resonance theory [122, 178], and spectral theory and spectral geometry [103 105, 381, 382, 389]. There is a sjgnificant distinction between the cases of ordinary and partial differential periodic equations. The main tool of the theory of periodic ordinary differential equations is the so-called Floquet theory [17, 94, 120, 156, 177, 267, 272, 389]. Its central result is the following theorem (sometimes called Floquet-Lyapunov theorem) [120, 267].

Bounded and Almost Periodic Solutions of Nonlinear Operator Differential Equations

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Author : A.A. Pankov
Publisher : Springer Science & Business Media
ISBN 13 : 9401196826
Total Pages : 231 pages
Book Rating : 4.4/5 (11 download)

Book Synopsis Bounded and Almost Periodic Solutions of Nonlinear Operator Differential Equations by : A.A. Pankov

Download or read book Bounded and Almost Periodic Solutions of Nonlinear Operator Differential Equations written by A.A. Pankov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: ~Et moi ... si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais poin t aUe.· human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non· sense', The series is divergent; therefore we may be able to do something with it. Eric T. Bell o. lleaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com· puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'e1re of this series.

Playing Around Resonance

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Author : Alessandro Fonda
Publisher : Birkhäuser
ISBN 13 : 3319470906
Total Pages : 309 pages
Book Rating : 4.3/5 (194 download)

Book Synopsis Playing Around Resonance by : Alessandro Fonda

Download or read book Playing Around Resonance written by Alessandro Fonda and published by Birkhäuser. This book was released on 2016-11-11 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an up-to-date description of the methods needed to face the existence of solutions to some nonlinear boundary value problems. All important and interesting aspects of the theory of periodic solutions of ordinary differential equations related to the physical and mathematical question of resonance are treated. The author has chosen as a model example the periodic problem for a second order scalar differential equation. In a paedagogical style the author takes the reader step by step from the basics to the most advanced existence results in the field.

Almost Periodic and Almost Automorphic Solutions to Integro-Differential Equations

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Author : Marko Kostić
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110641259
Total Pages : 372 pages
Book Rating : 4.1/5 (16 download)

Book Synopsis Almost Periodic and Almost Automorphic Solutions to Integro-Differential Equations by : Marko Kostić

Download or read book Almost Periodic and Almost Automorphic Solutions to Integro-Differential Equations written by Marko Kostić and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-05-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses almost periodic and almost automorphic solutions to abstract integro-differential Volterra equations that are degenerate in time, and in particular equations whose solutions are governed by (degenerate) solution operator families with removable singularities at zero. It particularly covers abstract fractional equations and inclusions with multivalued linear operators as well as abstract fractional semilinear Cauchy problems.

Ordinary Differential Equations

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Author : Nicolas Rouche
Publisher : Pitman Advanced Publishing Program
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.:/5 (44 download)

Book Synopsis Ordinary Differential Equations by : Nicolas Rouche

Download or read book Ordinary Differential Equations written by Nicolas Rouche and published by Pitman Advanced Publishing Program. This book was released on 1980 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.

Spectral Analysis of Differential Operators

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Author : Fedor S. Rofe-Beketov
Publisher : World Scientific
ISBN 13 : 9812703454
Total Pages : 466 pages
Book Rating : 4.8/5 (127 download)

Book Synopsis Spectral Analysis of Differential Operators by : Fedor S. Rofe-Beketov

Download or read book Spectral Analysis of Differential Operators written by Fedor S. Rofe-Beketov and published by World Scientific. This book was released on 2005 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigated in the book is the behavior of discrete eigenvalues which appear in spectral gaps of the Hill operator and almost periodic SchrAdinger operators due to local perturbations of the potential (e.g., modeling impurities in crystals). The book is based on results that have not been presented in other monographs. The only prerequisites needed to read it are basics of ordinary differential equations and operator theory. It should be accessible to graduate students, though its main topics are of interest to research mathematicians working in functional analysis, differential equations and mathematical physics, as well as to physicists interested in spectral theory of differential operators."

Periodic Differential Equations

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Author : F. M. Arscott
Publisher :
ISBN 13 :
Total Pages : 283 pages
Book Rating : 4.:/5 (65 download)

Book Synopsis Periodic Differential Equations by : F. M. Arscott

Download or read book Periodic Differential Equations written by F. M. Arscott and published by . This book was released on 1964 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Spectra of Random and Almost-Periodic Operators

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Author : Leonid Pastur
Publisher : Springer
ISBN 13 : 9783642743481
Total Pages : 0 pages
Book Rating : 4.7/5 (434 download)

Book Synopsis Spectra of Random and Almost-Periodic Operators by : Leonid Pastur

Download or read book Spectra of Random and Almost-Periodic Operators written by Leonid Pastur and published by Springer. This book was released on 2011-12-10 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last fifteen years the spectral properties of the Schrodinger equation and of other differential and finite-difference operators with random and almost-periodic coefficients have attracted considerable and ever increasing interest. This is so not only because of the subject's position at the in tersection of operator spectral theory, probability theory and mathematical physics, but also because of its importance to theoretical physics, and par ticularly to the theory of disordered condensed systems. It was the requirements of this theory that motivated the initial study of differential operators with random coefficients in the fifties and sixties, by the physicists Anderson, 1. Lifshitz and Mott; and today the same theory still exerts a strong influence on the discipline into which this study has evolved, and which will occupy us here. The theory of disordered condensed systems tries to describe, in the so-called one-particle approximation, the properties of condensed media whose atomic structure exhibits no long-range order. Examples of such media are crystals with chaotically distributed impurities, amorphous substances, biopolymers, and so on. It is natural to describe the location of atoms and other characteristics of such media probabilistically, in such a way that the characteristics of a region do not depend on the region's position, and the characteristics of regions far apart are correlated only very weakly. An appropriate model for such a medium is a homogeneous and ergodic, that is, metrically transitive, random field.

Almost Periodic Differential Equations

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Author : Arlington M. Fink
Publisher : Springer
ISBN 13 : 9780387067292
Total Pages : 336 pages
Book Rating : 4.0/5 (672 download)

Book Synopsis Almost Periodic Differential Equations by : Arlington M. Fink

Download or read book Almost Periodic Differential Equations written by Arlington M. Fink and published by Springer. This book was released on 1974 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: